According to the Daily Mirror, the Italian pace-setters are considering a bid for the 24-year-old Brazilian international when the winter window opens.
Dutch international Strootman was linked with United again this week after ex-PSV boss Dick Advocaat tipped him to move to a 'top club' like Manchester United.
He's been excellent since joining the Serie A leaders from PSV in the summer, but the long-term Old Trafford target is already being mentioned as a target for other big clubs.
As a result, the report claims Tottenham's battling midfielder Sandro could be the man to replace him in the Italian capital if he does elect to join United.
The Brazilian international faces fierce competition for a place in the Spurs midfield, with Paulinho, Mousa Dembele and the currently injured Etienne Capoue all jostling for just two starting spots.
But Sandro is in contention to start against Manchester City on Sunday as he continues to work towards full fitness having missed much of preseason.