Portugal left-back Coentrao was left out of Ancelotti's squad for their La Liga opener against Real Betis on Sunday, with the Italian boss revealing 'he has asked to leave'.
Coentrao has been linked with a number of Premier League teams, although he has indicated a desire to play in the Champions League, which could make life tougher for Tottenham to sign one of their targets.
Madrid paid more than £25m for the 25-year-old when he joined from Benfica in the summer of 2011 but Spurs are believed not to be willing to go above £17m to bring him to England.
Their interest in Coentrao comes at a time when talk continues over Gareth Bale, who has been a Madrid target for most of the summer.
Ancelotti said he was happy with his squad heading into the season-opener but admitted Bale would be a welcome addition as 'great players always bring things to a team'.