The 29-year-old attacking midfielder made 29 appearances across all competitions and registered two assists in a disappointing season for Madrid.
Isco, whose current Madrid deal will expire in 2022, also failed to make Luis Enrique's Spain squad for Euro 2020 this summer.
The Madrid star's future at Los Blancos remains uncertain, with the Spanish club potentially axing him to help reduce their wage bill.
Defensa Central now reports that Isco has 'been in touch' with Diaz amid growing interest from Milan.
Diaz, 21, made sporadic appearances for Madrid after leaving Manchester City in 2019 in a reported £15.5m deal, which could rise to £22m through add-ons.
The Spain international spent the previous campaign out on loan at Millan, but Madrid have reached an agreement for Diaz to spend the next two seasons at the San Siro.
Isco's potential availability this summer has also attracted interest from Premier League clubs Arsenal and Tottenham.
According to CalcioMercato, Madrid are willing to sell the former Malaga man for £21m.
However, the major obstacle for Milan in securing Isco's services is matching his hefty £5.9m salary at Madrid.
Milan are keen to reinforce their midfield options this summer after Hakan Calhanoglu's departure to fierce rivals Inter Milan.
Isco has been identified as a replacement for the 27-year-old Turkish playmaker, with former Madrid star James Rodriguez another reported target for Milan.
Rodriguez has become unsettled at Everton after the departure of Carlo Ancelotti to Los Blancos.
The 30-year-old Colombia international, who signed for the Toffees in 2020, has admitted that he is "missing Italy" amid speculation surrounding his Everton future.
Speaking on his Twitch stream, Rodriguez said: "I would like to play wherever they want me, I already played in all the leagues; I am missing Italy, it would be a good option."
Featured Image Credit: PA