Spanish newspaper Marca, as reported by talkSPORT, claims Leverkusen have lodged their second bid to recruit the 20-year-old star. They failed in their first approach during the summer window, but the report suggests they will make another bid in January.
Tottenham were strongly linked with the Spanish youth team international over the summer, with speculation suggesting he could be included in part of the package for Gareth Bale.
But Carlo Ancelotti rebuffed Tottenham's attempts to include Jese, who has been compared to Cristiano Ronaldo for his style of play.
He could be available next month though, with the young forward struggling for first-team football at the Bernabeu.
He's made seven substitute appearances for the La Liga giants this season, but is yet to start a league game. His lone league goal came against Barcelona in El Clasico.
But Tottenham have fallen behind Leverkusen in the race to sign him, with representatives from the German club meeting Real Madrid officials following their Champions League game against Real Sociedad earlier this week.