One spell level uses less than one page in a classical spellbook
Fifth edition tries to not force you to do administration chores like tracking encumberance or counting spellbook pages used, unless you enjoy it. Therefore, there is no hard limit on the numbers of spells you can put into your book in the rules. It could be arbitrarily many if you don't care for this part of the game.
However, if you do care, we can deduce at least an upper bound for traditional spell books.
There are four statements in the rules that are relevant for the amount of space in a spellbook. First, the wizard starting equipment on p. 114 PHB and the description of the spellbook on p. 153 PHB
You start with the following equipment, in addition to the equipment granted by your background: (...) A spellbook
Spellbook. Essential for wizards, a spellbook is a leather-bound tome with 100 blank vellum pages suitable for recording spells.
As all the equipment in the class descriptions refers to the equipment from chapter 5, the spellbook that a wizard starts with has 100 pages. It is not one of the fancy alternate spellbooks you could conceivably have.
There is no mention of needing to buy additional spellbooks to have room for your spells. This means, the spellbook of 100 pages you start out with must provide sufficient space to write all the spells you learn up to level 20.
Space dependence on level
Secondly, we also know that the ink a spell consumes is proportional to its level (page 114 PHB, also mentioned in the accepted answer):
You can copy a spell from your own spellbook (...) You need spend only 1 hour and 10 gp for each level of the copied spell.
Whatever the unit of space is, as the ink used to scribe it is proportinal to the spell level, the space the ink uses should be proportinal to the spell level, too.
Career levels known
Thirdly, the statement about adding spells to the book (p.114 PHB) and the wizard table tell us how many spell levels need to fit into the book:
At 1st level, you have a spellbook containing six 1st-level
wizard spells of your choice. (...) Each time you gain a wizard level, you can add two wizard spells of your choice to your spellbook. Each of these spells must be of a level for which you have spell slots, as shown on the Wizard table. On your adventures, you might find other spells that you can add to your spellbook (see the “Your Spellbook” sidebar).
The additional spells from adventures that can be copied into the book are optional, so we will ignore them. The spells gained from leveling are not. The upper bound of spell levels you can add to your book for a wizard are initial 6 first level spells from level one, plus two times the levels of the highest level spell you can learn in the wizard table for each additional character level, all the way up to level 20. This totals up to 184 spell levels. All of which will need to fit into your book.
Maximum page requirement per spell level
With all of this, we can put an upper bound on the pages a spell level can take up: it must be possible to fit 184 spell levels into a book of 100 pages. That means, at most a spell level can take up a little more than half a page (54.35% of a page).
If you went with the one page per level rule instead, you could expect that at the latest by spell level 7 the wizard would need to buy an extra book. If they find a good number of additional spells, much earlier (we used that rule and I had to buy one around character level 8).
Minimum page requirement per spell level
The rules do not provide a lower bound on how many pages a spell needs. You could go down to small fractions of a page -- or you could forgo traditional books and pages entirely (see Thomas's answer), if you are so inclined.
Purely to give some reference points: there are 829 levels worth of wizard spells in the PHB so to allow a wizard to collect all the spells from the PHB without needing a second book, each level could only take up less than an eigth of a page.
Considering that a wizard might find some but not all additional spells adventuring, if you even care about tracking pages, a good number could be half a page per spell level. This would leave room to add another 16 levels of spells to the book, without having to buy an additional book.