The Belgium international impressed towards the latter stages of last season as Palace comfortably avoided the drop to the Championship under then manager Sam Allardyce.
Last week it was reported Chelsea, who are preparing to allow striker Diego Costa to leave Stamford Bridge this summer, are interested in luring Benteke to the Premier League champions.
But now this summer’s big-spenders Everton have been credited with an interest and are looking at the 26-year-old as a replacement for Romelu Lukaku, who saw his move from Goodison Park to Manchester United confirmed on Monday.
Eagles boss Frank de Boer will be eager to keep Benteke at Selhurst Park and will want the former Aston Villa and Liverpool forward to lead the line at Palace next season.
Goalkeeper Wayne Hennessey hopes to remain at Crystal Palace ahead of his deal expiring after holding talks over an extension.
Burnley boss Sean Dyche says he will not be making a raft of signings this summer despite the demands of European football.