Pogba once again raised question marks over his relationship with Mourinho over the weekend.
Following Manchester United’s 2-1 opening day win over Leicester, the France midfielder was asked if he was happy at the club.
His response was: “There are things, and there are things that I cannot say, otherwise I will get fined.”
This comes after there were reports last season Pogba and Mourinho’s relationship had broken down.
Pogba has since been linked with a move away from Old Trafford.
ESPN FC pundit Paul Mariner was asked who Woodward should choose between the two.
Presenter Dan Thomas said: “If you were in charge of Manchester United, if you were Ed Woodward and you had to choose one or the other, who would you choose? Pogba or Mourinho?”
And Mariner says it should be the World Cup winner who Woodward should try to keep hold of the most.
“I would choose the top man, I would choose Paul Pogba,” the former Arsenal striker said.
“He’s the heart and soul of that football team.
“What he did at the weekend was borderline remarkable.
“As Jose Mourinho said, playing 80 minutes, scored the winner, brave enough to take it.
“When you’re the top man at a football club and you come out with a statement like that, well you just don’t, you don’t come out with a statement like that, if all’s rosy in the garden.
“So the undercurrent, the undertones here are far reaching.
“It’s very difficult to get inside people’s minds but it’s just shocking that he would come out with that statement.”
United’s next Premier League match is against Brighton at the AMEX this Sunday (4pm).