Imbula joined Stoke from Porto in 2016, with the Potters paying a club-record £18m fee for the midfielder.
The former France Under-21 international made 14 appearances for Stoke in the second half of the 2015-16 season, before appearing on a further 14 occasions for the Premier League club.
The 25-year-old represented Toulouse on loan last term, however, making 34 appearances for the Ligue 1 outfit.
According to RMC, both Newcastle and Palace have contacted the player's representative to ascertain whether he would be interested in a move this summer.
Imbula has a contract with his now-Championship club until the summer of 2021.