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The Frenchman joined United in 2016 for a then-world record fee of £89 million but a move to Spain has always lingered in the background.
Pogba is currently away on international duty with France and when asked about playing for 'Los Blancos' in the future, he didn't end the speculation.
"Many things have been said," the 27-year-old begun per talkSPORT.
"What can I say? Yes, all football players would love to play for Real Madrid. It is a dream for me, why not one day?
"I am in Manchester and I love my club. I am playing in Manchester, I'm having fun and I want to do everything to put the club where it deserves.
"I will give everything to the max, like my team-mates."
His contract with United is up at the end of this season but the club do have an option to extend it by an additional year.
The midfielder admitted there has been no contact with the hierarchy at Old Trafford regarding an extension.
"All football players would love to play for Real Madrid. It is a dream for me, why not one day?" :eyes:- Sky Sports News (@SkySportsNews) October 8, 2020
Paul Pogba also says there has been no contact from #MUFC over a contract extension: https://t.co/Ld5nFaHrpI
"No-one has told me anything," the World Cup winner continued.
"I have not spoken to [executive vice-chairman] Ed Woodward. We haven't spoken about a new deal.
"At the moment, I am in Manchester and I am concentrating about getting back to my best form.
"I think there will be a moment when the club will come and talk to me and maybe offer me something, or not.
"So far, nothing has happened. I can't tell you something that I don't know."
Pogba's comments come less than a week after United's humiliating 6-1 defeat to Tottenham Hotspur.
The 27-year-old gave away a penalty in the game as the Red Devils conceded six at home for just the second time since 1978.
United responded by making four signings on transfer deadline day, including Porto left-back Alex Telles and free agent Edinson Cavani.
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Featured Image Credit: Sky Sports & PA Images
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