As of the time that this post went live, Tottenham Hotspur have 27 players on the books who were assigned squad numbers this year, have played in competitive senior matches this year or will be assigned senior squad numbers shortly (Vlad Chiriches and Erik Lamela). One of those players is almost certain to be out the door shortly (Gareth Bale), but he also counts as a home grown player. Additionally, Christian Eriksen seems likely to be joining up.
If you're thinking that Tottenham are unlikely to make deals on transfer deadline day because of the current depth of their squad and their need to fit under squad limits ... well, think again. Spurs actually have a ton of flexibility heading into deadline day. That's mostly because the Under-21 rule is extremely liberal.
Players "under 21" don't have to be registered and don't count against Premier League squad limits, but that doesn't mean that players actually have to be under the age of 21 when registered. Anyone born after January of 1992 is "under 21" for the purposes of squad rules. That means that all of Erik Lamela, Tom Carroll, Zeki Fryers and, if he joins, Christian Eriksen, do not count against squad limits.
We also don't need Bale, Fryers and Carroll to reach eight homegrown players. Kyle Walker, Danny Rose, Aaron Lennon, Kyle Naughton, Andros Townsend, Jermain Defoe, Michael Dawson and Gylfi Sigurdsson are all homegrown.
If we register everyone currently on our books except for Bale, we come up with this squad:
Total: 23 total players, 8 homegrown
Tottenham could very well sell Gomes or let him walk on a free, which would leave another free spot for another non-homegrown player. Most teams don't have a third keeper more accomplished than Jordan Archer, so don't expect a replacement to come in. Spurs could, if they felt it necessary, purchase three more outfield players.
They could also hang on to Gomes and move some other players -- even homegrown ones. The squad rules don't require anyone to have eight homegrown players, they just require teams to have eight homegrown players if they're going to name a 25-man squad. Spurs could sell or loan one or both of Defoe and Sigurdsson and still register a legal squad without a problem.
The point of all this is to clarify that Spurs' current squad situation doesn't dictate any of their transfer activity over the next four days. I don't think anyone's expecting fireworks after Bale is sold and Eriksen is locked up, but Franco Baldini and Daniel Levy have plenty of wiggle room if they want to make further adjustments to the squad. Plenty of players -- of any age and homegrown status -- could still come and go.