Sanchez has spent the 2019-20 campaign on loan with Inter, scoring four times and registering 10 assists in 29 appearances in all competitions.
As it stands, the 31-year-old is due to return to Old Trafford this summer, but the Serie A outfit are keen to sign him on a permanent basis ahead of the 2020-21 season.
According to The Express, United have informed Antonio Conte's side that they will have to come up with a £15m offer in order to secure his services on a long-term basis.
The former Arsenal forward still has two years left to run on his contract with Ole Gunnar Solskjaer's side, placing the English giants in a relatively strong negotiating position, although Sanchez's huge wages are likely to prove problematic.
Inter secured the runners-up spot in Serie A on Saturday night courtesy of an impressive 2-0 victory at Atalanta BC, where Sanchez featured as a late substitute.