Isco has a £620million release clause in his contract and Spanish journalist Eduardo Inda says he has had offers to move to England.
"They [Real Madrid] consider that Isco is not involved in the group, that he is doing his thing, that he is having problems with his weight - so he is thinking of going to the Premier League,” he said.
“He has an offer from Chelsea and another from Pep Guardiola at Manchester City.
“I think that in a style of play like City’s he could do very well.”
Real boss Santiago Solari insists he has no problem with Isco (Image: GETTY)
However, Solari moved quickly to try and play down the rumours by claiming he does not have a problem with Isco despite freezing him out of the first team.
“Honestly, I think there's not really anything to talk about here,” he said.
“I spoke the other day. These are things that happen, they are decisions that have to be made. That's it.”
Isco was named on the bench once again for the 2-0 win over Valencia at the Bernabeu on Saturday night.
Dani Carvajal says Isco is one of the most popular players in the Real Madrid dressing room (Image: GETTY)
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He came on for the last ten minutes as a Daniel Wass own goal and a late strike from Lucas Vazquez claimed all three points.
Real moved up to fifth in La Liga and are now just three points behind leaders Sevilla, who travel to fourth-placed Alaves on Sunday (7.45pm).
The top of the table could not be closer and Atletico Madrid can reclaim top-spot temporarily with victory at Girona (3.15pm).
Barcelona will do likewise with a win at the Nou Camp against Villarreal (5.30pm).