Mundo Deportivo also claims that Mino Raiola, the player's agent, will try to work on the deal to take Pogba to the La Liga giants.
Shaw, who himself has suffered plenty of criticism from Mourinho in the past two seasons, then appeared to make the game safe when he fired low into the far corner to spark wild celebrations from his manager.
But the 25-year-old was made captain for his club's Premier League opener against Leicester City and was praised by Mourinho for his performance, which included the goal that set United on the way to a 2-1 win.
"What do you mean being the real Pogba?"
Following an impressive display from Pogba, Mourinho commented that a player "always feels more comfortable when he is happy".
"Man United have invested too much in Mourinho to sever those ties in the middle of the season".
Pogba was overlooked as the permanent successor to Michael Carrick as club captain, with Valencia instead getting the nod from manager Jose Mourinho - a decision that reportedly upset the midfielder. "I think it's the last time we speak about it, it's over, finished, the market is closed and no more talk about it".
"It's not a role that I give to myself. I haven't won the Premier League, I haven't won the Champions League, I haven't won the European Championship so there are more to win", he said. I know it's a great cup, it will stay in my mind, but I want to win all the trophies.
United fans purred at the presence of Pereira, Fred and Paul Pogba playing together in midfield and Andreas reserved some kind words for our World Cup victor, who played over an hour after less than a week of training. Paul Pogba can't play 90 minutes, Fred the same.
Mourinho left no doubt as to how much he valued Pogba's efforts on the night, adding: "Paul was fantastic - his contribution was unbelievable".
"I'll always give my best to the fans and my team-mates no matter what's going on", he wrote.
"Like I said, when you are comfortable, when people trust with everyone or confident, are good in the head, it's going to be easier".
Liverpool have splashed the cash in hope of catching City this time out, with Jurgen Klopp spending around £175m in the window.
Pogba said "everybody was on the same page" in the France dressing room, from manager Didier Deschamps to the staff and players. "We have to wait until the end of November to understand if we can fight for the title".