The Denmark international has struggled to make an impact since he left Tottenham for Inter in the January transfer window.
Inter are now open to offloading Eriksen next month and according to The Sun, United are ready to make their move.
The report claims that Inter are demanding a £27 million transfer fee, which is around £10m than what they paid to sign him from Spurs earlier this year.
United, meanwhile, are said to be keen on signing another attacking midfielder with Pogba keen to leave Old Trafford.
Eriksen had been linked with a move to United last year before he opted to join Inter.
Paris Saint-Germain and Arsenal have also been linked with a move for Eriksen, while reports in Italy claim that Inter would be open to a potential swap deal involving Granit Xhaka.
Speaking at the weekend, Conte admitted that Inter are open to letting some of the fringe players leave in order to get more playing time elsewhere.
‘There are things to consider in an objective way, from outside you don’t see real things, both the directors and I knew all the difficulties we had at the beginning of the season,’ Conte told DAZN.
‘We go ahead, hoping to improve something, some players can leave to have more game time. We may become less deep, but more functional.’