The Argentina international is a wanted man after his exploits for Antonio Conte's side.
ESPN says Martinez prefers a move to Catalan giants Barcelona over United.
Ole Gunnar Solskjaer can now add the 22-year-old to his list of missed striker targets.
Erling Braud Haaland rejected a move to Old Trafford last month in favour of joining Borussia Dortmund.
Inter paid Racing Club £20m for Martinez in 2018.
Barca would be prepared to pay big for Martinez as they want to replace the ageing Luis Suarez.