The Chilean had been on loan at Inter, and now Fabrizio Romano reports the forward will join on a permanent basis.
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Despite having two years left on his contract at Old Trafford, United appear keen to get Sanchez off their wage bill by letting him leave for free.
The 31-year-old earns a reported £400,000-a-week at United, having signed from Arsenal when swapping with Henrikh Mkhitaryan in January 2018.
The willingness to forego any transfer fee outlines United’s intentions to offload Sanchez, who struggled during his 18 months at the club before moving out on loan.
At Inter, Sanchez made 22 Serie A appearances, scoring four times and assisting a further nine as Inter finished second behind Juventus.
Conte says he is committed to three-year project with Inter
Inter Milan coach Antonio Conte is committed to a three-year project with the club, he said on Monday, two days after his highly critical and typically outspoken outburst raised questions over his future with the Serie A outfit.
Conte, in his first season in charge, led Inter to a second-placed finish, their best performance for nine years, but then publicly slammed his employers immediately after Saturday's 2-0 win at Atalanta.
FC Internazionale coach Antonio Conte issues instructions to his players during the Serie A match between Atalanta BC and FC Internazionale at Gewiss Stadium on August 1, 2020 in Bergamo, Italy
Image credit: Getty Images
He said the club had failed to back him and his players in the face of heavy criticism and that his efforts had not been recognised.
However, on Monday, he appeared to soften his stance, telling the ANSA news agency: "I am committed to a three-year project with Inter and, as I always have done in my life, I will work hard and fight with all my strength and everything in my power to make it a winning project."
Inter's season is still not over as they are involved in the Europa League and face Spanish side Getafe in a single leg last 16 tie on Wednesday.
Additional reporting from Reuters