The Lions have been closely linked with the Brazilian international over the past month.
Rafael was left out of United’s tour of the USA and has fallen down the pecking order following the Red Devils signing of Matteo Darmian.
The Brazilian international’s agent Cassiano Perreira recently confirmed that his client was in talks with numerous clubs around Europe.
“His contract expires in June 2016 and the coach, Van Gaal, said he isn’t counting on him, so the player wants to leave and we are talking with more than one club about this,” Pereira told Italian website Tuttomercatoweb.
United could release the right-back on a cut-price deal as the 25-year-old full-back currently has just one-year left on his current deal.
Rafael would join fellow Brazilian players Felipe Melo and Alex Telles should he join Galatasaray. Brazil national team legend Claudio Taffarel is also the teams goalkeeping coach.
The 25-year-old provided one assist and scored one goal in 17 appearances for the Manchester United last season.