The 30-year-old has been in strong form for his Turkish club during the 2023-24 campaign, scoring eight goals and registering three assists in 21 appearances in all competitions.
Batshuayi's contract is due to expire in June, though, and there is currently speculation surrounding his future, with a number of clubs believed to be interested in his signature.
According to The Sun, Rangers are currently in talks with the Belgium international, who has been identified as the Scottish outfit's number one target in the final third of the field.
The report claims that the Gers are looking to hand Batshuayi an initial deal until the end of the season to see how he performs for the club before committing to a long-term contract.
Batshuayi has only had four permanent clubs during his career, but he has had five separate loan spells, most recently at Besiktas during the latter stages of his time at Chelsea.
Meanwhile, according to Football Insider, Wolverhampton Wanderers are continuing talks with West Ham United over a January move for experienced forward Danny Ings.
The 31-year-old has struggled to make his mark for the Hammers during the 2023-24 campaign, failing to find the back of the net or register an assist in 18 appearances in all competitions.
Wolves are said to be looking to sign Ings on loan for the second half of the season, but there is believed to be disagreements with West Ham over the loan fee and contribution of Gary O'Neil's side to his wages.
Talks are allegedly continuing, and there is a hope that an agreement can be found, but West Ham first need to secure a replacement, as Michail Antonio remains injured, while Mohamed Kudus is set to link up with the Ghana squad for the Africa Cup of Nations.
Ings, who has a contract at the London Stadium until June 2025, has only managed three goals and two assists in 40 appearances for West Ham in all competitions.
Staying in the Premier League, Fulham have allegedly made a €20m (£17.2m) offer for Atletico Madrid centre-back Caglar Soyuncu.
According to Italian journalist Gianluca Di Marzio, Fulham are currently battling Roma for the Turkey international's signature, with Atletico willing to sell for the right price this month.
Atletico are also said to be open to letting the centre-back leave on loan, but a permanent departure could occur, providing that the Spanish outfit's asking price is met.
Soyuncu made the move to the Red and Whites last summer on a free transfer, with his contract at Leicester City coming to an end.
However, the 27-year-old has found it difficult to secure regular action at Wanda Metropolitano, featuring just six times in all competitions, and he could be set for a return to the Premier League.
Soyuncu made 132 appearances during his time at Leicester, including 98 outings in England's top flight.