Sterling, 31, hasn’t played a game for Chelsea since Mauricio Pochettino was in charge but reportedly turned down several offers to leave in the summer.
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It’s understood that Sterling has no interest in leaving London with his family settled in the capital where he earns around £350,000 a week.
According to Caught Offside, both Palace and Leeds are willing to offer him a chance to revive his career in the upcoming January transfer window.
The winger still has 18-months left on his contract at Chelsea with the club increasingly keen on getting his high wages off their books.