Leicester and Tottenham are first and second respectively in the Premier League table at the moment, while West Ham are fifth.
Arsenal are currently third in the standings, and Keys has backed the Gunners to finish in the top four.
“I suspect Arsenal will make it - but who finishes 4th?” the former Sky Sports presenter wrote on his website. “Right now, if they can hold it altogether, I reckon the Hammers just might.
“That too would be reward for a fantastic season - so far. On form I make Leicester, Spurs and West Ham the best 3 teams in the P Lge.”
Leicester, Tottenham and Arsenal are the most likely candidates to make up the top three, but the fourth spot is up for grabs.
Manchester City currently occupy that position, but West Ham, Manchester United, Southampton and Liverpool all are eyeing it.
West Ham have been superb this season, and the football Slaven Bilic’s side have played at times has been breathtaking.
There will be questions whether the Hammers can maintain their current form until the end of the season, but with Dimitri Payet in red-hot form, everything is possible for the London outfit.