The Serbian is out of contract and it does not appear he will be offered new terms.
He has impressed in recent weeks in central midfield, but Calcio Mercato suggests his future lies elsewhere.
His wage demands may be an issue, with Milan reportedly saying they will not cave into his demands.
The 31-year-old wants a significant contract, as it may be his last one in football.
There is still a chance he stays at United, but it would be dependent on manager Ole Gunnar Solskjaer wanting to keep him around beyond this term.