The News of the World says Didier Drogba, Frank Lampard, Michael Essien and Ricardo Carvalho are all considering their futures and Bridge insiders fear they will quit if Roman Abramovich keeps faith with the Israeli boss.
Many Blues players have grown exasperated by Grant's man-management techniques and his apparent lack of tactical know-how. They believe a winning run in the Premier League has merely papered over the cracks and that the humiliating Wembley defeat had been on the cards.
One source said: "There are a lot of players asking a lot of questions about Grant.
"If he's here next season, then a lot of the big names will be out the door.
"There is no real faith in him - and many of the players don't think he's capable of making the big decisions.
"There's been a lot of talk about Frank Rijkaard replacing him but Abramovich doesn't show any sign of getting rid of Grant.
"If that stays the same, then a lot of the players think the club will either stand still or go backwards - and they won't hang around for that."