The Morocco international spent the 2023-24 campaign on loan at Manchester United, making 30 appearances in all competitions, but the Red Devils turned down the chance to sign him on a permanent basis.
Fenerbahce have recently been heavily linked with Amrabat, with Man United said to have now ruled themselves out of the running for the experienced midfielder.
However, according to transfer expert Fabrizio Romano, Everton have also made an approach, with the Toffees keen to sign him before the end of the transfer window.
Fiorentina are believed to want in the region of €15m (£12.6m) for the 28-year-old, who has entered the final year of his contract with his Italian club.
Ipswich 'in advanced talks' over Ogbene deal
Meanwhile, according to The Athletic, Ipswich Town are in advanced discussions with Luton Town over a move for Chiedozie Ogbene in the latter stages of the transfer window.
The 30-year-old, who has been capped on 20 times by Republic of Ireland, scored four times and registered one assist in 30 Premier League appearances last season.
Ogbene has started all three of Luton's Championship matches this season, but he was not in the squad for Tuesday's EFL Cup second-round clash with Queens Park Rangers.
Ipswich are allegedly closing in on a move for the attacker, with the newly-promoted Premier League club preparing to spend more money in the latter stages of the transfer market.
Ogbene, who represented Rotherham United ahead of his switch to Luton in July 2023, is capable of operating in a number of different positions in the final third of the field.
Southampton 'fail with Fellows bid'
Elsewhere, Southampton have allegedly had a £10m offer for Tom Fellows rejected by West Bromwich Albion.
The 21-year-old came through the youth system at West Brom, and he has represented the Baggies on 49 occasions in all competitions, scoring five goals and registering seven assists in the process.
The Englishman has three assists in three Championship appearances at the start of this season, including two in his side's 2-1 success over Stoke City last weekend.
There has recently been transfer speculation surrounding Fellows, and according to journalist John Percy, Southampton placed a £10m offer on the table earlier this week.
However, it is understood that West Brom were quick to reject the bid, with the Baggies demanding 'a big fee' for a player who is thought to be attracting the attention of a number of other Premier League clubs.