The 20-year-old striker has not started for United in the Premier League since late December and British media reported that the situation is causing Southgate concern as he prepares to name his squad for friendlies against Netherlands and Italy.
"You know, if the national coach trusts him, he selects him," Mourinho told reporters ahead of United's league trip to Crystal Palace on Monday.
"You have the example of (Sergio) Romero, who is the second goalkeeper at Manchester United and the first goalkeeper for such an amazing football country like Argentina.
"In your own country, you have examples of players who play even without scoring a goal in the Premier League. So it's up to Gareth Southgate. It doesn't matter if he plays or if he doesn't play for Manchester United."
Despite competition from Alexis Sanchez, Anthony Martial, Jesse Lingard and Juan Mata, Rashford has made 38 appearances for United in all competitions this season, including 25 in the league.
"Because Marcus had such an impact in the beginning, probably people are expecting him to play even more than he does and score even more than he does and to perform even more than he does... But that's not so simple," Mourinho added.
"At his age, what he's doing is more than enough, and the experience that he's getting at every level is more than enough, for us to be happy with what we think is going to be his future."
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
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