The 23-year-old has struggled for game time at Los Blancos, with Ronaldo, Gareth Bale and Karim Benzema all ahead of him in the pecking order. And things have got worse for Jese after the club re-signed Alvaro Morata.
And Spanish media MARCA have revealed that Real are prepared to listen to offers for the Spaniard, which has alerted the Gunners. Arsene Wenger is looking for a new forward, after being snubbed by Jamie Vardy earlier in the summer, and now missing out on Gonzalo Higuain.
The Argentine has joined Juventus after a record breaking year in Serie A, scoring 36 goals in one campaign.
Jese scored 5 league goals from 28 La Liga outings, but only 7 of those were starts. He also netted in the UEFA Champions League, scoring in a 2-0 win away at AS Roma.
The 23-year-old has a good relationship with boss Zinedine Zidane, but MARCA reports that the French boss has suggested Jese should consider other opportunities away from the Santiago Bernabeu.