The Independent says Deschamps, who captained France to glory in the 1998 World Cup and Euro 2000, is now one of the names in the frame to replace Mourinho.
Deschamps began his coaching career with Monaco before joining Juventus. But he resigned from the Italian club in May 2007 and is currently unemployed.
He spent a year with Chelsea as a player in 1999-2000 - winning the FA Cup.