The daily newspaper state that the Super Lig giants are preparing a move for the 34-year-old.
Terry has been criticised following Chelsea’s slow start to the season winning just one point from their opening two games. The former England international has a year left on his contract with the Blues.
The Mail goes onto state that Fenerbahce will offer Terry £2.5 million per season plus a lucrative signing-on bonus.
Terry was substituted off the field at half time during Chelsea’s 3-0 defeat at the hands of Manchester City.
The 34-year-old has spent his entire career at Stamford Bridge and has 78 caps for the England national team.
Fenerbahce have snapped up Robin van Persie from the Premier League during the transfer window.
Van Persie was not however, the only United player to join the clubs ranks as Luis Nani also made the move to Istanbul.