Reporting via their verified Twitter account, it is claimed that the 23-year-old is wanted by the Super Lig side in the winter transfer window.
They wrote: “Galatasaray will meet Rangers for Ianis Hagi at half-time [January]. Istanbul-born Hagi can come back to his home town at half-time.”
Hagi has made no secret of his desire to one day play for the Turkish giants where his dad, Gheorge, became a club icon.
The Rangers forward said in May [via Emanuel Orsu’s Twitter profile]: “One day, I’d like to play for Galatasaray. It’s a club I love, I grew up with that club in my heart. I was born there.
“I don’t know what the future holds, but I have feelings for that club.”
Clearly, Hagi has dreams of playing in a Galatasaray shirt, and it appears inevitable that he will one day adorn the red and yellow of the Istanbul-based side.
Galatasaray will also play in European competition post-December as they secured qualification to the Europa League knock-out stage last week with a 4-2 win over Marseille.
However, after 14 Super Lig games, Gala are currently sitting in eighth, just three points ahead of 16th-placed Kayserispor who occupy the final position above the relegation zone.
The club doesn’t quite perhaps hold the attraction it did in the ’90s and the start of the 21st century.
Hagi may also wish to pursue a move to a ‘top-five’ league when he does leave Rangers, with a Premier League move mooted as a possibility.
But, for now, he appears settled at Rangers and Giovanni van Bronckhorst has started him in both of his first two games in charge.
With Rangers targeting a second successive Premiership title and set to continue their journey in Europe, a January switch looks unlikely.