The 29-year-old midfielder is now a free agent after his contract at Serie A giants Juventus expired on June 30.
Rabiot made 212 appearances for Juve across all competitions during a five-year spell at the club, scoring 22 goals, providing 14 assists and winning four trophies including the 2019-20 Serie A title.
The France international stated last month that he has "not made any decisions yet" about his club future and was focused on representing France at Euro 2024.
Les Bleus have since been eliminated at the semi-final stage by Spain and speculation over Rabiot's future has now intensified.
Rabiot unlikely to stay at Juve or join Milan?
According to Calciomercato, the prospect of Rabiot staying at Juventus and signing a new contract cannot be ruled out, but the Turin-based giants have no intention of raising their salary offer between €7m and €8m per year over a two-year deal.
It is thought that Juve are not prioritising Rabiot's renewal as they have now signed two centre-midfielders at the start of the summer transfer window in the form of Douglas Luiz and Khephren Thuram from Aston Villa and Nice respectively.
Rabiot may consider staying put in Italy, with AC Milan said to have held 'several meetings' with the midfielder's agent and mother Veronique Rabiot to gauge his interest in a potential move to San Siro.
However, as things stand, problems lie with the player's salary and commission demands, and Milan are now believed to have turned their attention to signing Monaco's Youssouf Fofana.
Three European giants to battle for Rabiot?
Rabiot could instead test himself abroad, with Calciomercato reporting that Real Madrid, Liverpool and Bayern Munich are all 'plausible' destinations for the Frenchman.
Real Madrid, who already have French duo Aurelien Tchouameni and Eduardo Camavinga on their books, are known to be in the market for a new centre-midfielder following the retirement Toni Kroos.
Liverpool, meanwhile, have begun a new era under head coach Arne Slot and are expected to recruit at least one new midfielder this summer following the departure of Thiago Alcantara who, like Kroos, has decided to hang up his boots.
As for Bayern, they have announced the signing of top target Joao Palhinha from Fulham, but they could look to sign another midfielder if in-demand Joshua Kimmich decides to seek pastures new.
Both Manchester United and Tottenham Hotspur have also been credited with an interest in Rabiot, but the midfielder is not thought to be high on either club's list of targets at present.