According to AMK Spor (h/t Nihat Emre Kocaaslan of Sport Witness), the Turkish giants are keen to strengthen this area of the side, with Badou Ndiaye poised to join Stoke City. Fellaini, whose contract at Old Trafford is set to run out at the end of the season, is said to be an option.
It's reported that while Galatasaray have held talks already about possibly securing Fellaini on a pre-contract, the departure of Ndiaye has prompted them into trying to get a midseason deal done.
Fatih Terim, the Galatasaray boss, is said to be a massive admirer of the Belgium international, so much so that they're reportedly ready to offer the 30-year-old a four-and-a-half-year contract.
Here's a look at how the story was reported, per Sport Witness:
Fellaini has been a dependable option for United boss Jose Mourinho over the past couple of seasons, although he's missed a decent portion of this season due to injury.
In the past, the former Everton man has split opinion among the United fanbase. On the ball, he's not the most agile, while at times his lack of discipline has led to needless pressure being put on the rest of the team.
However, when used in the right way, Fellaini can be a major threat against any team. The midfielder is exceptional in the air, is so hard to bustle off the ball and can provide an excellent focal point in the final third.
Mourinho has spoken highly of the player many times previously, and when asked about the player's future recently, he reaffirmed his desire to see Fellaini stay at the club, per Simon Stone of BBC Sport:
It's easy to envisage Fellaini wanting a new challenge. After all, while he's a useful footballer to have around, Paul Pogba, Nemanja Matic and Ander Herrera are all ahead of him in the midfield pecking order.
At Galatasaray, while the standard of the Turkish Super Lig doesn't rival the Premier League, he'd be getting regular minutes and would be a crucial part of Terim's setup. As noted in the report, Fellaini would also be getting paid well, with Galatasaray said to be ready to offer him an annual salary of £3 million after tax.
With United competing for the UEFA Champions League, Premier League and FA Cup still, there will be occasions when Mourinho calls on Fellaini should he stay. Subsequently, perhaps a summer departure would suit all parties.