The Spanish midfielder was an integral part of Ancelotti's title-winning Bayern team in 2017, making 25 league appearances as the Bavarian club won the Bundesliga with a 15 point lead over second-placed RB Leipzig.
And according to Italian football journalist Gianluca Di Marzio, the Italian manager is still a keen admirer of the 29-year-old, despite being sacked by Bayern in September of last year. However, the German champions will not allow Martinez to leave if Napoli do make an offer for the Spanish international.
Despite this interest from Ancelotti and Napoli, the need for a central midfielder is not a urgent issue to resolve following the arrival of Real Betis midfielder Fabian Ruiz for a reported €30m fee. The 22-year-old is seen as a replacement for Jorginho, who is set for a Premier League move to one of Manchester City or Chelsea.
Indeed, Napoli are more in need of a full back capable of playing on either side, Di Marzio claims that I Partenopei have identified Bordeaux defender Youssouf Sabaly as the perfect fit for this position. The Senegalese player started all three of his country's World Cup group games over in Russia, and Ancelotti is looking to agree personal terms with the player, before approaching the Ligue 1 side with an offer.
Should a move for Sabaly break down, then Red Bull Salzburg's Stefan Lainer and PSV Eindhoven's Santiago Arias will be targeted as alternative options.
Ancelotti has recently taken over the reins at Stadio San Paolo following the departure of Maurizio Sarri, who is set to become Chelsea's new manager this week. The 59-year-old has taken his new side to a pre-season training camp in the city of Trento in the north of Italy.