Martinez has no plans to leave Old Trafford.
The Argentine defender is still recovering from a cruciate ligament injury sustained in February and may not return to action until 2026.
Reports from Italy suggest Napoli is keen to strengthen its defense and has identified Martinez as a potential target.
The club previously secured Scott McTominay from United at a bargain price, and he played a crucial role in their title-winning campaign.
However, Napoli may struggle to replicate that success, as Martinez is reportedly content at United and has no desire to move.
Before his injury, the 27-year-old was a key figure in Ruben Amorim’s defensive setup and is regarded as one of the squad’s leaders.
While Martinez is unlikely to depart, Napoli could have better luck pursuing Alejandro Garnacho, who has fallen out of favor under Amorim.
The Italian side attempted to sign him in January but failed to reach an agreement.
United is set for a busy transfer window as Amorim reshapes his squad.
The club has lowered its asking price for Garnacho, but he appears determined to remain in the Premier League, with Chelsea showing interest.
Several other players could also be on their way out, including Antony, Jadon Sancho, and Marcus Rashford, who are expected to leave after returning from loan spells.
Additionally, United is reportedly open to offers for Kobbie Mainoo, while Rasmus Hojlund has attracted interest from Inter Milan, potentially paving the way for a move to Italy.