The 26-year-old's contract with Fiorentina is due to expire next June, and he is widely expected to be on the move during the current market, with Man United thought to be at the head of the queue for his services.
Liverpool and Aston Villa have also been linked with the Morocco international, while a recent report claimed that Al-Ahli are also keen to bring him to Saudi Arabia.
Man United are thought to be preparing to step up their interest in Amrabat once a deal for Rasmus Hojlund has been secured, with the Denmark international allegedly completing his medical on Tuesday night.
However, it is widely believed that the Red Devils will look to sell Fred and Donny van de Beek before potentially bringing in Amrabat to boost their midfield options.
A recent report claimed that the 20-time English champions have already agreed to meet Fiorentina's £30m asking price for the Moroccan.
However, Amrabat has played down suggestions that a move away is close, with the midfielder speaking after his team's 4-0 friendly win over Grosseto on Tuesday.
«I don't know if I'm leaving… maybe I can stay here at Fiorentina,» he told reporters.
The midfielder was heavily linked with a move away from his Italian club in January off the back of playing a key role in Morocco advancing to the semi-finals of the 2022 World Cup.
Earlier this year, Barcelona were thought to lead the race for his signature, but the Catalan outfit have since cooled their interest, with Man United now at the head of the queue.
Amrabat made 49 appearances for Fiorentina during the 2022-23 campaign, helping
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