The Romanian continues to be linked with a move away from Ibrox despite only joining the club in January 2020 from Belgian side Genk for a fee of around £3m, signing on a permanent basis after an initial loan move.
The 22-year-old, who is the son of former Barcelona legend Gheorge, has started the season in good form, scoring two goals in three appearances despite picking up a slight injury that saw him miss the Champions League third qualifying round first leg defeat to Malmo and the 1-0 loss at Dundee United.
He scored in the 3-0 win over Livingston on the opening day of the Scottish Premiership season and the 5-0 victory over Dunfermline in the Premier Sports Cup last Friday. In total, he has made 50 appearances for Steven Gerrard's side, scoring 10 times.
Speculation has circulated that Rangers could look to cash in by selling the playmaker before the end of the summer transfer window, with a need to sell players to balance the books following their Champions League exit.
Turkish newspaper Fanatik claim that Galatasaray have failed with a €4million offer for Hagi, with Sevilla and Lazio also seeing bids in the region of €7million rejected.
The report suggests the Ibrox side are holding out for €11million - around £9.3million - for the player.
Hagi is expected to be named in the squad as Rangers host Alashkert in the Europa League play-off first leg on Thursday.