Unlike the rest of European football's other major leagues, clubs in Turkey can sign new players up until close of business on Friday.
As in the summer, that may result in some of the biggest clubs from the nation targeting players from Premier League clubs and other high-profile divisions.
Defending champions Galatasaray, in particular, have money to spend after generating in the region of €35m for the sales of Sacha Boey and Cedric Bakambu.
Defender Serge Aurier and forward Carlos Vinicius have since been acquired as natural replacements for each, yet only a small fraction of the recent income as been spent on the pair.
The possibility remains that Galatasaray, who are level on points with Fenerbahce in the top flight and competing in the Europa League, may now look to make at least one statement signing.
According to Fotomac, there is an interest in securing the signature of Eriksen before the end of the week.
Eriksen can claim to have enjoyed a productive campaign in terms of game time, making 11 starts and eight substitute outings in Premier League and Champions League fixtures.
However, the 31-year-old has remained as an unused substitute during the recent victories over Wolverhampton Wanderers and West Ham United respectively.
With Kobbie Mainoo, Casemiro and Scott McTominay ahead of him in the pecking order at present, it is unclear whether the Denmark international will receive regular game time going forward.
Sofyan Amrabat is another option in the engine room at a time when United have no European football on their schedule, raising the question of whether Eriksen could be sold for the right price.
The report claims that Galatasaray view Eriksen as 'their main target' for the remainder of the transfer window, but it is unclear whether the playmaker would entertain a move.
Just 17 months are left on his contract at this stage, with United seemingly yet to decide whether they will negotiate a renewal in the future when they may want to boost their FFP position and reduce their wage bill.