Lukaku left United for the San Siro in a £76.5million deal earlier this month.
The Daily Mail says he has “been working on Sanchez every day" to link up with him again in Italy.
They also state the former Everton and West Brom forward has told the 30-year-old “Milan is a far more beautiful place to live than Manchester" as he attempts to persuade him to make the reunion.
It looks like Lukaku will soon get his wish as Sanchez closes in on an initial loan.
He has already agreed terms with Inter and chosen to wear the No.7 shirt.