United shelled out a then-world record £89million to sign Pogba back from Juventus in 2016 but the France international has struggled to match the lofty expectations placed upon him.
The 27-year-old enjoyed an impressive 2018-19 season, scoring 13 goals and supplying nine assists in 35 Premier League appearances – his best return in a single top-flight campaign.
However, he has struggled with injuries since, being involved in four goals (one scored, three assisted) in 19 league appearances since the start of 2019-20.
Pogba expressed a desire for a new challenge ahead of that campaign but a move away from Old Trafford is yet to materialise.
A return to Juventus and a switch to Madrid have been mooted, and Pogba would relish the chance to play for LaLiga's champions.
"All footballers would love to play for Real Madrid. It is a dream for me. Why not one day?" said Pogba while on international duty with France on Thursday.
"[But] I am in Manchester and I love my club. I perform in Manchester, I have fun and I want to do everything to put the club back where it deserves to be.
"I will give my all, like my team-mates and the club. We all want to come back to the best level."
Pogba was part of France's World Cup-winning squad in 2018 but has only lifted the Europa League and EFL Cup since returning to United.
His contract at Old Trafford is due to expire in June, though there is an option for it to be extended by a further year.
Pogba is yet to hold any talks with the club over his future but expects to have them soon enough.
"There's been a lot of talk, and I prefer not to. I prefer to be focused on football and especially my recovery," said Pogba.
"I have not spoken with [executive vice-chairman] Ed Woodward. There has been no mention of a renewal.
"For now, I'm in Manchester and I'm thinking about getting back to my best.
"I think there will be a time when the club will come and talk to me and maybe offer me something, or not. So far, nothing has happened."