I know it's not technically possible since some of them play each other in the next three or four match days, but here's the top seven if all of them (Top Seven) win all of their (upcoming) fixtures, having played 23 games in total:
59 | Manchester City
51 | Liverpool
48 | Tottenham
44 | Chelsea
44 | Arsenal
40 | West Ham
38 | Manchester United
Manchester City (22) plays their 23rd game against Southampton.
Liverpool (21) play their 22nd and 23rd games against Crystal Palace and Leicester City.
Tottenham (18) play their 19th, 20th, 21st, 22nd and 23rd game(s) against Leicester City, Chelsea, Southampton, Wolves and Manchester City, respectively — and in that order.
Chelsea (23) has played 23 games already.
Arsenal (20) plays Burnley, then Wolves and then Brentford.
West Ham's (22) next (23rd) fixture is against Manchester United.
Manchester United (20) visits Brentford, and then hosts West Ham next, and then we visit Burnley for our 23rd fixture.
Well, fuck.