The 25-year-old is no longer in coach Hansi Flick’s plans and Bayern have made him available for €35m.
The English club have already contacted Tolisso’s entourage to discuss the details of a hypothetical deal.
Inter coach Antonio Conte is a big fan of Tolisso’s profile and tried to sign him in 2017 while in charge of Chelsea.
Tolisso has long had a weakness for the Premier League, which may give Man United an advantage.
United and Inter will contact Bayern Munich in the coming days to begin formal negotiations.
Tolisso, a 21-time French international, has made seven Bundesliga starts this season with a further six sub appearances.