It is claimed Conte is an admirer of Palace talisman Benteke, who is close friends with Eden Hazard but has been out since September with a serious injury, and could move for the Belgian this winter.
A hamstring injury has meant Barkley has not featured at all for Everton this season.
Caretaker manager David Unsworth has said "he would love" the midfielder to stay at Goodison Park, per Neil Jones at the Liverpool Echo. He is a top talent. he could be one of the all-time greats'.
He struggled to force his way into Chelsea's first-team last season, primarily playing back-up to in-form Diego Costa, but then scored the goal that clinched the Premier League title away at West Brom in May.
If, as expected, Chelsea sign a player to bolster Conte's attacking options, £33million signing Batshuayi may be sent out on loan to gain more experience and develop his game.
Conte and co return to action after the worldwide break by making the trip to West Brom.