Bournemouth have already been identified as many as candidates to go straight back down, not least due to their lack of transfer business, and Keys thinks they will be relegated.
Fulham meanwhile have a reputation as a yo-yo club and have failed to stay up the last two times they were promoted to the Premier League, though they have made several prominent signings this summer.
Keys picked Nottingham Forest as the team that will thrive after promotion, though he did caution they will reach just about ten wins.
The veteran anchor thinks Southampton will also suffer the drop and cautioned fans of the three teams he thinks will go down that they should be worried.
“Of the new-boys I think Forest are best equipped to survive”, the former Sky Sports anchor wrote on his blog.
“The City Ground will be a hard place to visit, but they’ll still struggle to win 10 games.
“I reckon they’ll have enough – just about enough – if they can win a few at home.
“Fulham? Down.
“Bournemouth? Down.
“If you pushed me I’d go with Southampton to make up the relegated three.
“If you’re looking for a surprise struggler – its got to be Leicester.
“And for the record – I’ve had two of the bottom three correct in each of the last two seasons.
“So be worried if you support those teams.”
Leicester fans will be hoping that they can get a few signings in the door, but it will depend upon player sales.
Fulham start the campaign by hosting Liverpool, while Bournemouth welcome Aston Villa and Southampton travel to Tottenham Hotspur.
