Sky Sports says United are in ongoing talks with Pogba over a new contract.
The France midfielder's current deal expires next summer and will be eligible to sign a pre-contract agreement elsewhere in January if a new contract with United isn't agreed.
With United keen to avoid losing Pogba for free for a second time, they are eager to extend at Old Trafford with talks ongoing.
Pogba's future at United has been the subject of speculation for several years, with agent Mino Raiola suggesting the midfielder is 'unhappy' at the club and 'needs a change of scenery' amid interest from other clubs.
When asked about his future following France's 2-2 draw with Portugal at Euro 2020 on Wednesday, Pogba said: "I'm not thinking about my future, I'm only focused on the Euros."
The report indicates that while several clubs hold interest in the 28-year-old, no official bids have been made.