The Spaniard is not in manager Mauricio Pochettino’s plans after a failed move to Manchester United last summer.
Following Luke Shaw’s injury, Manchester United were reportedly keen on signing the Chelsea left-back on loan last summer.
But the Red Devils ended up signing Tottenham’s Sergio Reguilon after the move for Cucurella fell through for a number of reasons.
The Spanaird moved to Stamford Bridge in a £62m deal from Brighton last summer but has found life difficult at the west London club.
His only game for Chelsea under Mauricio Pochettino so far this season came in the 2-1 Carabao Cup win over AFC Wimbledon.
And The Sun is now reporting that the defender is keen to leave the club when the January transfer window opens in a few months time.
Cucurella, who has played 34 games for the Blues, is reportedly being monitored by Real Madrid as he could be heading back to Spain in a loan move.