Out of our current squad, these are the first team players over 21;
'Keepers: Hart, Wright, Caballero.
Defenders: Zabaleta, Sagna, Kompany, Demichelis, Mangala, Kolarov, Clichy.
Midfielders: Nasri, Navas, Fernando, Fernandinho, Yaya, Silva.
Strikers: Aguero, Bony, Dzeko, Jovetic
That's 20. You're allowed a maximum of 17 foreign players so out of those 20 we need a minimum of 3 to be homegrown;
Homegrown: Hart, Wright and Clichy
We can name as many U21s as we like, Sterling is the most notable. Other players likely of being promoted to the first team squad are Lopes, Denayer and possibly Iheanacho.
That right away is an official squad of 20 by Premier League rules but 23/4 players to realistically choose from.
Factor in the likely departures of Dzeko and Jovetic then that would allow us to sign 2 foreign players. Say, off the top of my head, De Bruyne and Pogba. Any "foreign" transfers outside of that would require one in, one out. Or we could sign players like McCarthey with 5 free HG spots to fill up if we want.
*Disclaimer: I know I'll have messed up somewhere in my reasoning.