The 23-year-old’s current deal runs until 2024 and according to the player’s legendary dad Gheorghe the club want to reward him with an extension.
Hagi has started eight of the nine games new boss Giovanni van Bronckhorst has managed since taking over from Steven Gerrard.
He should reach 100 games for the club at some point this season.
The son of Romanian football hero Gheorghe Hagi, Ianis has been linked with numerous clubs during his time at Ibrox.
His father recently confirmed the player “loves it" at Rangers before spending time with him in Glasgow during the festive period.
Speaking to media in Romania after the trip, Gheorghe revealed he was reliably informed the Ibrox club were planning on giving the player a new deal.
"We were fine, we felt good together, we talked, the family needed us to stay together," he said.
"I stayed for a little while, a week. He looks good, he's motivated.
"By the way, that's what I heard and I think it's from a reliable source, that they want to renew the contract.
"Not as it is written in the press here. He played very well.
"He had an extraordinary year, very good, he is appreciated there and from good sources I think they want to renew the contract."
Hagi has three goals and four assists in 25 appearances in all competitions this season.
Under Van Bronckhorst he has played either on the right of midfield or through the middle.