Having spent last season on loan at Crystal Palace, Loftus-Cheek shone at the World Cup earlier this summer with England.
The midfielder has been overlooked by Maurizio Sarri, managing just 22 minutes for Chelsea in the first two Premier League games of the season.
A handful of Spanish clubs are interested in the 22-year-old who could seal a deal with their window closing on August 31.
And the Daily Mirror claim Loftus-Cheek will look to reject any new deal offered by the Blues and try and get regular football elsewhere.
When asked why he left Loftus-Cheek out against Arsenal, Sarri said: “It depends on the position on the pitch.
“I prefer to have on the bench two wingers, and only one midfielder.
“So it depends on this.
“Not any other situation.
“I needed on the bench one goalkeeper, one full-back, one centre-back, maybe two midfielders and only one winger.
“But [in training on Friday] I preferred vice versa, two wingers and one midfielder.”
Meanwhile, Ian Wright thinks Loftus-Cheek faces a tough challenge to convince Sarri with Jorginho, N’Golo Kante and Mateo Kovacic ahead of him in the pecking order.
“I would love to see Loftus-Cheek to see if he can break into the first XI,” Wright said last week.
“He’s got to try and play.
“This is the only situation where a player has not stayed at his parent club for the time he’s been there apart from the youth team.
“He’s too good to sit around.
“He’s now got to get Jorginho, Kante and Kovacic out of the way.”