Las Palmas president Miguel Ángel Ramírez admits they face missing out on Jese.
The PSG attacker is available and keen on a move to Las Palmas this month.
However, Ramirez concedes there's a Premier League club which is threatening to trump them for the Spaniard.
"I've been talking to his agent today and there's an English club that wants to pay it all," he said.
Middlesbrough and Sunderland are being linked with Jese.