Jese is on-loan at Stoke from PSG, but has struggled to settle due to complications for his newly born son in Spain.
Las Palmas coach Paco Jemez is hopeful of adding quality to his squad in the winter and made clear in an interview with El Larguero that Jese's quality would be a significant boost.
"I told the president that it's up to him to bring Jese," he explained.
"If we are going to make the effort to bring in a player of such quality, he must be an example to everyone in every aspect.
"If Jese comes, it must be as a fully committed player."