The striker is said to be content with life in London and looking for a new home in the capital.
What's more, Benteke only arrived at Selhurst Park last summer in a £27 million deal, and he has three years remaining on the contract he signed, so the Eagles will be keen to keep hold of their primary goal-getter.
He netted 17 times last season in 40 matches, and he has scored 66 in 154 Premier League appearances.
That puts him only slightly behind the goals-per-game ratio of his compatriot, and the man he would be replacing at Goodison Park, Romelu Lukaku, who has scored 85 goals in 186 Premier League outings.
The 26-year-old shares several attributes with Lukaku including his powerful physique and strength in the air, per Squawka Football:
Squawka Football @Squawka
Most headed Premier League goals since 2012/13: Olivier Giroud (25) Christian Benteke (23) Romelu Lukaku (18) Aerial threats. 💪 https://t.co/8RsDih3zWn2017-7-9 08:31:01
While he would not be a completely like-for-like replacement for the former Everton man, and he's not quite at the same level, he would be fairly close.
Bleacher Report's Matt Jones has reservations over him, though:
Matt Jones @MattJFootball
Would love Dzeko or Giroud. Benteke not so much; probably would be the most expensive and is the most injury prone of three #EFC2017-7-10 21:15:26
There are indeed some question marks over him and how worthwhile the deal would be.
Benteke does not appear to be ready to move on to what would be his fourth club in three years, and Palace will likely drive his price up if any interested parties make an approach. So while he would not be a bad choice for Everton, there are probably better and potentially cheaper alternatives out there.