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In the final year of his contract, Pogba is said to have turned down an extension at United and is not interested in committing himself to the club.
Real Madrid and Paris Saint-Germain would appear to be two potential suitors for the World Cup winner, who could be available this summer for around £50 million.
But Le10Sport say that a shock move to Liverpool is possible. Mino Raiola, Pogba's controversial agent, has apparently offered the Frenchman to the Reds and told them a deal could be done in the current window.
Jurgen Klopp is on the hunt for a new central midfielder after seeing Gini Wijnaldum leave on a free to PSG in the summer and Pogba's name has been mentioned "behind the scenes" according to the report.
Liverpool aren't overly keen on doing a deal this summer but could be interested in snapping him up for a cheaper fee in January, by which point his contract will be mere months away from expiring.
In April 2018, ahead of a derby where Pogba scored twice in a stunning 3-2 win, Manchester City boss Pep Guardiola claimed Raiola had offered him Pogba and Henrikh Mkhitaryan in the January window that had just been.
There has been little activity between Liverpool and United in terms of first-team transfers over the years.
A player has only moved between the two clubs on nine occasions, with Phil Chisnall's £25,000 from United to Liverpool way back in 1964 the last instance it happened.
In 2007, Sir Alex Ferguson famously refused to sell Gabriel Heinze to Liverpool because he did not want to sell to a direct rival.