The report states that Hamza Hamzaoğlu wants to sign a right-back over the summer and that Rafael has been added to the shortlist.
The Lions have made strengthening at right-back a priority over the summer transfer window after Tarık Çamdal failed to settle in last season.
Former Arsenal right-back Emmanuel Eboue has already parted ways with Galatasaray and Çamdal is also expected to leave.
Sabri Sarıoğlu will remain the only the first-team right-back unless another fullback is signed.
Galatasaray already have two Brazilian players – Felipe Melo and Alex Telles – and former World Cup winner Claudio Taffarel is the teams goalkeeping coach.
Rafael’s future as a United looks extremely bleak after he fell out of favour with head coach Louis van Gaal and struggled to hold down a regular first-team spot.
Galatasaray won the league title for a record 20th time last season and booked a place in next seasons Champions League group stages.