The 21-year-old, son of the legendary Gheorghe Hagi, has spent the season on loan at Ibrox from Genk.
However, in recent months there have been doubts over whether Rangers can afford to sign Hagi permanently.
Rangers’ balance sheet can breathe now though, after they struck a big money partnership with Castore.
According to Corriere dello Sport, citing Pro Sport, Rangers are now able now pay the €5m it will cost to keep Hagi.
The Scots will want to close a deal quickly amid Serie A interest in Hagi. Lazio are admirers of the attacking midfielder, and Cagliari have gone public about wanting him.
Cagliari coach Walter Zenga said on Monday: “I’ve been following the progress of Ianis Hagi for three years. Of course, I want to bring him to Cagliari.
“Three years ago, I was manager of Crotone and I tried to bring Ianis to the club on loan from Fiorentina, where he was wasn’t getting a game.
“But Gheorghe Hagi wouldn’t sanction the move because he wanted him to return to Romania. He is a huge talent and would have coped at Crotone 100 per cent.”
Hagi has made 12 appearances in total for Rangers this season, scoring three goals.
The 10-cap Romania international was previously on the books at Fiorentina in Serie A before spells back home and with his current club Genk in Belgium.