You should really ask them why.
Not out of the assumption that they're trying to pull a fast one on you, but because you're the person who keys all the encounters in the world, hostile and otherwise. If your players are building up a collection for anything other than their own satisfaction - because they're not really going to find a buyer for monster weapons, monster weapons aren't magic*, and it's likely they're not even trained in them - knowing their motive will let you either give them a bit of what they expect or tell them it's not possible.
Heck, if they are just building up a collection for their own satisfaction, that's still useful to know, because it's more interesting to collect interesting things, and when you key an encounter you can spend a little time thinking about what to tell them about the weapons afterwards. Even a handful of terrible goblin daggers can still be interesting if, say, they've got weird patterns on the metal that seem to flow from one blade to the next, and when you spend some time at camp fitting them all together, it turns out they were all torn from some fallen caravan guard's armor and then sharpened up.
That said, here are some rules cornerstones that might help you build something more, if they need something more.
Monsters don't [W].
That is to say, the attacks in the statblock that notionally use their weapons shouldn't be assumed to reflect what their weapons can do. I mean, sometimes they do track, or at least parts of them do track, but when an angel of vengeance hacks you with a longsword and gets an icefire chaser, the icefire comes from the angel of vengeance, not its longsword.
Monsters are big and small.
Monsters larger than Medium or smaller than Small wield weapons appropriately scaled for their size, and sometimes a statblock will track the damage for those larger-sized weapons. Rules for weapon size and damage are on p.220 of the PHB, but a key takeaway from those rules is that PCs usually can't use weapons that are larger than them.
There are no guaranteed buyers, but...
Also on p.220 is a little note about not really being able to find buyers for regular equipment without GM approval. But if your players are collecting weapons with the expectation of some eventual payoff, well, we have a word for that.
That word is sidequest.
Or maybe even plain ol' quest. I don't know how you'll end up building this out. But if the PCs happen to meet an eccentric collector who just can't get enough monster weapons, or a wandering scholar who curates a weird weapons collection and would be happy to share tales of mysterious wisdom from forgotten lands, p.122 of your DMG has some guidance on how to track and reward that. Basically it's just rerouting some of the expected wealth per level down a different path, in the form of cash money direct or perhaps a boon of knowledge that works like a magic item.
*Monster weapons aren't magic, but...
p.174 of your DMG talks about giving monsters magic gear and how it affects the statblock, which you might want to do if you're going to give the players some magic gear and they're fighting monsters that would be inclined to use it. The basic takeaway is that a monster using gear on-tier for its level only gets a +1 to the relevant bits.
But, if you squint, there's the concept that "monsters have gear from one tier down", which can play productively into certain motivations for collecting weapons, like "turn their weapons against them" or "melt them down into a sweet new sword".
Not that every vengeful specter dagger is going to discharge its icy spite like a vial of alchemist's frost (Adventurer's Vault p.25) from one tier up, but if you want to toss in one that will, take that cost off of a treasure parcel and you're good to go. Not that there must be a smith who works with legion devil steel, but if your players are really het up to reinforce their gear with it, you have some idea of how much they'll need to collect and what it might do.
You should really ask them why.
But all of the extra things to do with monster weapons over and above "you guys have some monster weapons I guess" are extra things. If people don't want to engage with them, you're just throwing some make-work into your campaign that nobody finds fun. So ask them why. Then you can give them a game and a story to fit their reason.