Yacine Adli was closely linked with a move to Arsenal earlier in the transfer window but ended up staying at PSG.
Adli could still be on the move but to Super Lig champions Galatasaray instead.
Turkish sports newspaper Fotomac report that the Lions want the 21-year-old on a loan deal.
Per the source, the club have sent officials to France for talks over a temporary move that would see Adli receive first-team football.
The PSG youngster is unlikely to be used a first-choice player for the senior side this term.
Galatasaray would be able to offer Adli first-team and Champions League experience next term.
The youngster did opt to stay at PSG earlier this summer despite reports claiming he was close to striking an agreement with Arsenal.
French journalist Loic Tanzi told Get France Football.
“Yacine’s has been particularly exceptional case, at a time when many young players are leaving PSG,” he said.
“A few clubs had been interested in him, notably Arsenal.
“It depends on the source – some of them were saying that he’d agreed to sign but then turned around and decided to stay at PSG, but those closer to him said that it wasn’t a U-turn and that he hadn’t agreed anything with Arsenal – he simply had the two options on the table but decided to stay at PSG.
“This is a specific case where you have to be careful, as you could have rushed things and said that the transfer was done, as I did, but in fact nothing had been signed.”
Galatasaray have already signed one player this summer, Henry Onyekuru from Everton.
The Lions are focused on temporary moves as a way around Financial Fair Play pressure to curb spending.