The 23-year-old joined the French giants in a deal worth roughly €25 million (£19.5m), after having just one year remaining on his deal with Real Madrid.
However, Jese – who came through the Real Madrid academy and was used sparingly throughout his time there – has struggled for minutes at Paris Saint-Germain this season.
Like a number of Unai Emery’s signings over the summer, the Spaniard has struggled to really adapt himself to life in Paris and he has been linked with a return to La Liga, with Las Palmas reportedly keen.
And in what appeared like a clear admission that Jese was not the right signing for PSG, Al-Khelaifi admitted the future was bleak for the winger.
“When you make a mistake, it’s better to try to correct it than to live with it,” Al-Khelaifi told Le Parisien, when asked about a potential move to Las Palmas for Jese.
“So if we’ve made mistakes, we’ll try to correct them. The door isn’t closed.”
Jese has managed just nine league appearances this season for Emery’s struggling PSG team, with eight of those showings coming off the bench.