Darmian, who played all 90 minutes of Manchester United’s 2-1 win over Leicester City, has been linked with a move to Benfica.
While Rojo, who only signed a contract extension with the club in March, has been the subject of a loan deal for Turkish giants Fenerbahce.
However, Mourinho would like both defenders to remain at Old Trafford for now.
Darmian is needed following the injuries to Antonio Valencia and Diogo Dalot.
Rojo will stay, after United failed to sign a centre-back on deadline day.
Signup for FREE news updates, latest information and hottest gists everyday