Zinedine Zidane is desperate to sign the French midfielder, and tried to get his man this summer.
The centre-midfielder was apparently keen to leave for the Bernabeu, and admitted that he wanted a ‘new challenge’.
However, United played hardball and demanded £150million for the star they paid £89m for in 2016.
Now, they are keen to tie down the midfielder to a new long-term contract – according to The Standard.
Pogba’s brother, Mathias, recently told Radio Marca that the 26-year-old is still keen to leave, throwing the potential new contract into doubt.
“Zidane wanted players, he didn’t get them,” he said.
“I have no doubt that he’s going to do the work he needs to do in order to get the team back to the level he wants.
“I like Zidane and he likes my brother, everyone knows it.”
Pogba will enter into the final year of his contract at the end of this season, but United have the option to extend the deal for another year.
Young forward Mason Greenwood will also reportedly be offered a new deal, after impressing when coming up through the youth ranks at Old Trafford.
The striker is set to start against Astana tonight in the Europa League, as Ole Gunnar Solskjaer looks to integrate the 17-year-old into his first-team squad.
Speaking at his pre-match press conference, Solskjear claimed the young star is one of the best finishers he has seen.
“He’s still very young but he’s maturing and he’s developed so much since I came in,” Solskjaer said.
“His appetite for football is growing. I don’t want to put too much pressure on him apart from go out there, enjoy yourself and work hard.
“When you’ve got strikers who can score goals, you should never lose the hunger of scoring goals. Never lose the appetite of creating chances and be ready to take yours.
“Mason is one of the best finishers I’ve seen and I’ve played with quite a few decent ones.”