Liverpool have long retained an interest in signing the Ligue 1 star.
The Reds missed out on him in the summer when the winger opted to move to PSG from Real Madrid.
However, he has found life in France tough, scoring just two goals from 14 games.
Jese Rodriguez has struggled for form at Paris Saint-Germain
Free transfers: 12 star players available in the summer
Mon, January 23, 2017
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John Terry (Chelsea)
Liverpool were keen to sign Jese Rodriguez from Real Madrid in the summer
His struggles have led to talk that he could be about to move to the Premier League.
But Spanish newspaper Marca claim the winger will snub interest from English clubs in favour of a return to Spain.
The 23-year-old is said to be close to moving to Las Palmas on loan.
Aitor Karanka wanted to bring Jese Rodriguez to Middlesbrough
A deal could even be announced this as early as this afternoon.
Middlesbrough were also hopeful of signing Rodriguez this transfer window.
But though manager Aitor Karanka has a good relationship with the star it was not enough to persuade him to move to the Riverside.