According to The Mirror, the Inter attacking midfielder is rated at £48million – and so far the Red Devils have failed to match that price.
And now, according to reports, the Blues also monitoring the winger’s situation.
The 28-year-old midfielder scored against United in pre-season in Singapore.
The Premier League side head coach Jose Mourinho is desperate to land one more signing this summer with a winger his main priority.
So he could ask chief executive Ed Woodward to go back to Milan with a higher offer.