The 30-year-old goalkeeper has one year left on his contract with AC Milan, which has not been renewed due to ongoing contract negotiations.
As a result, Maignan could potentially be signed by Manchester United in a lower-cost deal, given the current situation.
The club is looking to revamp its goalkeeping position, having recently signed Senne Lammens from Royal Antwerp.
Andre Onana, who was transferred to Trabzonspor after Lammens' arrival, is unlikely to return to Manchester United, while there are still doubts about Altay Bayindir's future with the team.