The 27-year-old signed for Everton from Mainz in a deal worth £25m in 2019 but has suffered from various injuries that have plagued his time at Goodison Park.
Gbamin, an Ivory Coast international, has only featured eight times for Everton and is currently on loan at Trabzonspor in the Turkish Super Lig.
The midfielder has only one year left on his contract and was expected to return to Finch Farm at the end of the season but has since told his agent that he "doesn't want to come back to Everton".
"We will have to find another project for him," his agent Bernard Collignon told BBC Sport.
"Jean-Philippe is so disappointed with everything that has happened and how things have not worked out for him," he added.
"I am the one who chose Everton for him because it would have been a stepping stone to move on elsewhere.
"There was interest from Arsenal, Tottenham and even Jurgen Klopp wanted to sign him for Liverpool six months before but now Jean-Philippe wants to go back to Germany."
