"The key for us is not the relationship with Jose, it's the relationship with Marcus," Southgate told reporters on Tuesday.
"I didn't speak to Mourinho about it. I let him know where I was heading with it at the end... If I am trying to keep Jose happy that's going to be, let's say, fairly difficult.
"I have got to make decisions that are right for England seniors long-term. I'm always mindful of what is right for the players," Southgate added.
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"Respectfully, none of the managers are going to be around in 10 years - or it's very unlikely - and I think people like Rashford will be.
"We want a good working relationship with the clubs, of course we do, but they have got their own objectives and have got to make decisions that are right for them, and I have got to make decisions that are right for England."
Southgate was full of praise for the 19-year-old Rashford after he helped United win the League Cup and Europa League.
"Rashford has won more than I won already... He is a lad who, whatever you asked him to do, he would do."
England play Scotland in their Group F World Cup qualifier on June 10 and face France in a friendly on June 13.
(Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford)
