The Serie A giants are being linked with a second approach for the Italy right-back, whose game-time has dramatically reduced since Jose Mourinho took over in 2016.
United rejected Inter's attempt to land Darmian on loan for the season last summer.
Inter instead borrowed Croatia star Sime Vrsaljko from Atletico Madrid for the term.
The Italians can buy Vrsaljko for £16million in July but so far the World Cup finalist, 26, has failed to impress.
And Darmian is seen as the solution for Inter after falling 11 points behind Serie A leaders Juventus.
Roma have also been linked with a January move for the 29-year-old, who joined United from Torino for £12.7m in 2015.
Darmian has been increasingly sidelined after playing 39 and 29 games respectively in his first two seasons at Old Trafford.
After 17 appearances last term, he has featured just twice this campaign.
Inter sporting director Piero Ausilio is said to be especially keen on returning him to Serie A, where he made his name.
Darmian launched his career with big rivals AC Milan before joining Palermo in 2010.
And after joining Torino he became one of Italy's top defenders, even being named the national team's player of the year for 2014.
Darmian has won the Europa League, FA Cup and League Cup with United but must be itching for regular starts.
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