Pogba is set to enter the final year of his deal and will be able to negotiate with clubs outside the Premier League from January before a possible free transfer move in time for the 2022-23 season.
This summer is United's last chance to receive a significant fee for the midfielder but sources have told ESPN there has been no firm contact from any of Europe's major clubs and there remain doubts about whether Real Madrid, Barcelona or Juventus could afford the financial outlay needed to sign the World Cup winner without including players as part of the deal.
Sources close to Pogba's camp have told ESPN that those clubs, and Paris Saint-Germain, would all be interested if he was available for free in a year.
Agent Mino Raiola has gone on record to say Pogba will not sign a new contract at Old Trafford but sources have told ESPN United have not given up hope that the 28-year-old will extend his stay.
There are, however, fears he could delay any decision beyond the summer in an effort to bring other bidders to the negotiating table.
If fresh terms cannot be agreed and there remains no market to sign Pogba this summer, United face the prospect of losing their £89.3 million record signing for nothing.