The spell locate object states:
"Alternatively, the spell can locate the nearest object of a particular kind, such as a certain kind of apparel, jewelry, furniture, tool, or weapon."
I'm not sure if a magical portal would class as an "object" for this definition?
Portals can be many things, and only some of them happen to be objects in the way the game defines object. The DMG explains this (p. 45):
"Portal" is a general term for a stationary interplanar connection that links a specific location on one plane to a specific location on another. Some portals function like doorways, appearing as a clear window or a fogshrouded passage, and interplanar travel is as simple as stepping through the doorway. Other portals are locations-circles of standing stones, soaring towers, sailing ships, or even whole towns-that exist in multiple planes at once or flicker from one plane to another.
So naming "portal" as your kind of object will not work, as portals are not a kind of object. "Kind of" implies a subset, and magical portal is not a subset of object.
What the spell allows you to look for is a kind of object. So you could try to find a portal if you happened to know what kind of object it was on. Let's take the wardrobe from the Chronicles of Narnia as an example: here you could look for a wardrobe.
How specific you can be in describing that object is left to the DM to adjudicate. For example, it is not clear whether you could name a "wardrobe that acts as a portal" or a "magical wardrobe". If your DM allows that, you could find it if it is in range. If the DM does not allow it, you may be out of luck looking for that portal in a furniture store, but it may still work if the portal is on the only object of that kind in range. In neither case could you find the way to Narnia if you did not know the portal was a wardrobe by just asking for a "portal".
The second level spell Warp Sense (from the Planescape: Adventures in the Multiverse rules) includes the following: -
For the duration, you sense the presence of portals, even inactive ones, within 30 feet of yourself.
As the spell is the same level as Locate Object, it seems unreasonable from a balance perspective to allow Locate Object to detect magical portals specifically. It also has a much shorter duration (up to one minute) and a much shorter range (it detects portals within 30 feet).
Otherwise, I agree with Nobody's assessment; that it would be reasonable to look for the physical object that a portal is summoned within/on/adjacent to, as long as you knew what that object was.
First we need to have an idea of what kinds of things spells can target, because in order to understand whether or not something counts as an object for the purposes of this spell, it will be helpful to be able to answer, 'if it is not an object, what else can it be?'
Spellcasting (Targets):
A spell's description tells you whether the spell targets creatures, objects, or a point of origin for an area of effect (described below).
Thus besides objects, we know that spells can also target creatures and points in space. Lest you think this is an exhaustive list, remember the rule of specific over general:
Choose one creature, object, or magical effect within range.
Even though a "magical effect" is not a creature, object, or point in space, and thus not something a spell can target by the general rules of spell targeting, the specific rules of dispel magic say that it can target magical effects, and so it can.
While still not exhaustive, this is a pretty good list of candidate categories. Locate object targets objects only, so is a portal an object, or is it a creature, a point in space, or a magical effect?
Planar Portals (DMG 45 - emphases mine):
"Portal" is a general term for a stationary interplanar connection that links a specific location on one plane to a specific location on another. Some portals function like doorways, appearing as a clear window or a fog-shrouded passage, and interplanar travel is as simple as stepping through the doorway. Other portals are locations - circles of standing stones, soaring towers, sailing ships, or even whole towns-that exist in multiple planes at once or flicker from one plane to another. Some are vortices, joining an Elemental Plane to a very similar location on the Material Plane, such as the heart of a volcano (leading to the Plane of Fire) or the depths of the ocean (to the Plane of Water).
From this description it is clear that there are different kinds of portals. All (planar) portals are connections between different planes, but while some function like "doorways" (being an empty area in space), others are vortices, and still others are locations - locations as small as a sailing ship to as large as a town.
All portals seem to be 'magical effects', and the ones that "function as doorways" are perhaps that and nothing more. Some seemed tied to specific places but not physical structures, so something like a vortex might best be described as a 'point in space'. But the portals described by the DMG as "locations" are not so much locations in a spatial sense as in a dramatic sense - they are linked with physical structures, and some of them are even mobile (like a sailing ship).
For those portals that are tied to physical structures, "object" seems to be a pretty good description of what they are - at least it is better than the other candidates. You could split hairs and say, "the standing stones are just a physical structure around which the portal manifests, they are not the portal itself - the portal itself is a magical effect". That would be fair, but then it would be equally fair for the user of locate object to specify their "nearest object of a particular kind" as 'the standing stones around which the portal is manifesting'. Note here it is of great help to know what you are looking for. Locate object could help you find the particular 'standing stones around which a portal is manifesting' on a vast field crowded with megalithic monuments, while not permitting you to wander about a city detecting anything that might be a portal, because you could not naively describe the object to which a portal might be affixed.
The DMG says that:
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone, not a building or a vehicle that is composed of many other objects.
This seems to place an arbitrary limit on the size or complexity of objects, such that rules like Ghosts of Saltmarsh say that sailing ships are not objects, rather they are collections of objects. Unfortunately, there is no consistency to these definitions, so (for example) a much larger Spelljamming ship is treated by the Spelljamming rules as an object! Personally, I think that objects exist at the scale of game interactions, and that what is treated as an object can change in different situations. However, even in a game with a more literal interpretation of what an object is, careful wording of the locate object spell should be able to pick out such things - again, presuming you already know something about the portal in question. 'I try to locate the mast of the sailing ship that is serving as the location of the portal,' should do, for example.
