The 27-year-old played under Toffees boss Sam Allardyce at Selhurst Park last season and finished the campaign with 15 goals from 36 Premier League games.
With Everton failing to adequately replace Romelu Lukaku in the summer and currently lacking an out-and-out striker, The Mirror claims that Benteke is seen as the solution at Goodison Park.
The report goes on to claim that Allardyce will have to sell before he starts recruiting new players after the club's sizeable outlay under former manager Ronald Koeman last summer.
Everton spent just over £142m in the last transfer window, though the sale of Lukaku to Manchester United for £76m and other outgoings reduced the net outlay to £45.75m.
Benteke has scored 18 goals in 53 appearances for Palace since his 2016 move from Liverpool.