The Spanish champions made an offer of £45m, plus Andre Gomes and Yerry Mina, for Pogba on Monday, according to Sky in Italy.
United could do a lot worse than attempting to bring the 27-year-old to Old Trafford although there would be competition for his signature.
Willian has suggested he would be happy to stay at Chelsea for the 2018-2019 but the 29-year-old has left the door ajar for a reunion with Mourinho.
The Swans, who were relegated from the Premier League last season, want £12m for the 26-year-old Ghana forward.
Pogba's agent travels to force move
Jose Mourinho tells ESPN FC that the World Cup was the flawless habitat for Paul Pogba as he could 'only think about football '. "This season, especially after the World Cup that he's had, he's going to start expressing himself a lot more".
But it appears that Pogba has been stirred by Barcelona's interest.
"It's down to the manager to get the best out of him, setting the team up and setting Pogba up in the right way to achieve the best", said the former England central defender. Pogba, a key member of the French team that won the World Cup in Russian Federation last month, was part of United's youth set-up but, short of first-team opportunities, opted to join Juventus in 2012.
Below we take a look at the three players United could target, if the worst comes to worse and they do lose Paul Pogba this summer.
Manchester United's hunt for the centre-back Jose Mourinho craves continues as the transfer deadline edges closer.
Romelu Lukaku and Marcus Rashford have since returned from their World Cup exertions but both are unlikely to be fit enough for 90 minutes against Leicester, possibly leaving Sanchez as the focal point of United's attack.
The club has had to deny the claim that Pogba sent a text message to Woodward demanding he be allowed to leave.