That's according to La Liga expert Guillem Balague, who instead suggests Middlesbrough could make a loan move.
Liverpool have been linked with a move for the out-of-favour forward this month.
But Balague has put those rumours to bed and says Middlesbrough are keen to take Jese on loan.
Liverpool are reportedly not interested in signing Jese Rodriguez
Aitor Karanka is understood to want to take Jese on loan at Middlesbrough
"It is not true that @LFC is after Jese (PSG). On the other hand, @Boro would love to get him on loan. Other clubs interested," Balague tweeted.
And the Spanish football expert echoed his opinion on Sky Sports and suggests a deal could materialise in the next days.
"There are different teams after him, but one that really wants him is Aitor Karanka's Middlesbrough," Balague told Sky Sports.
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— Guillem Balague (@GuillemBalague) January 23, 2017
"I don't think a decision has been made and there are other teams interested so we will have to see in the next few days how that develops."
Jese spent five years with Real Madrid before joining PSG in 2016 for £21m.
But the 23-year-old has started just once in Ligue 1 this season and is expected to earn a love move away from the French capital this month.