The England international has been in-and-out of the line-up for the Red Devils this campaign, but manager Ruben Amorim recently said that he is perfect for his back three.
Talks are ongoing over a new long-term deal with a pay-cut but as things stand, his £190,000 per week contract expires at the end of June next year.
United have the option to trigger an extension clause for another 12 months, but the club prefer to negotiate a new deal with a decent salary cut.
It is now revealed that Napoli are showing interest in signing Maguire following the success of former United teammate Scott McTominay.
Conte has the habit of signing Premier League based players for his Italian teams and he is open to working with Maguire at the Naples outfit.
The Serie A side are prepared to open talks with Maguire at the turn of the year if United do not trigger the extension clause in his contract.