The Morocco man was one of the standout midfield players at the 2022 World Cup and put in a series of dominant displays to help the Atlas Lions become the first-ever African semi-finalists.
Amrabat's exploits could to land him a move to a Champions League club in 2023, with both Liverpool and Tottenham expected to battle for his signature in January.
Liverpool apparently view the 26-year-old as a cheaper alternative to Enzo Fernandez and Jude Bellingham, while Tottenham boss Antonio Conte knows Amrabat well from his time in Serie A.
Spurs were understood to have been tracking the Fiorentina man in the summer, but a move did not materialize, and Tuttomercatoweb reports that PSG have now entered the race.
Amrabat shares an international dressing room with Parisiens right-back Achraf Hakimi, who was another integral member of Morocco's dazzling run in Qatar, which culminated in a fourth-placed finish.
The report states that Amrabat and Hakimi share an "excellent" relationship, and the latter has already expressed his desire to bring the Fiorentina man to the French capital to Kylian Mbappe.
The attacker has had a significant say in transfers since signing his bumper new deal, and Mbappe appears to have given his approval for PSG to begin the groundwork on a deal.
Amrabat is only under contract at Fiorentina for another 18 months, although La Viola can extend his deal until 2025 and are determined to agree fresh terms with the Moroccan.
However, should he decide against extending his stay in Italy, Fiorentina would reportedly accept a fee greater than €30m (£26.4m) to sanction a sale in the next year.
Amrabat's brother and agent Nordin Amrabat has already issued a public plea to PSG to make a move for the midfielder, telling L'Equipe: "Nasser Al-Khelaifi, if you read my words, take my brother!"
Amrabat previously represented Utrecht, Feyenoord, Club Brugge and Hellas Verona before signing for Fiorentina in 2020, and he has one goal to show from 78 games in a Viola shirt.
The 26-year-old helped Fiorentina make the Europa Conference League with a seventh-placed finish in Serie A last season, and he has already made 20 appearances for his club in the current campaign.
PSG reinforced their midfield with several signings during the summer window, where Fabian Ruiz, Vitinha, Renato Sanches and Carlos Soler all penned permanent deals with the Ligue 1 champions.
Vitinha has often been paired with Marco Verratti - who is apparently on the verge of signing a new four-year contract - in Christophe Galtier's midfield, where Danilo Pereira is also competing for minutes.