The Romanian international has two years left on his contract at Ibrox and will return to Glasgow after the Euros.
He spent last season on loan at La Liga, where he played sparingly, and he appears unlikely to be included in Philippe Clement’s plans for the coming season.
And Hagi appears to be resigned to leaving Ibrox after disclosing that he has left it up to his representatives to decide his future while on international duty.
He said: “My focus is on the Euros. I had talks with my agents and the pressure is on them.
“They know what I want for my future, it’s a pretty important summer for me from all points of view. I told them before going to the national team what I wanted.
“I expect them to work as well as possible, to find the right team and the right manager for me.
“I can’t say if I’ll be at Rangers or somewhere else. My future depends on my agents.”
Hagi appeared in 146 games following an initial loan period and scored 24 goals, but his growth was limited by a knee injury that sidelined him for a year.
Meanwhile, Giovanni van Bronckhorst, the former Rangers manager, is back in football management.
The Dutchman has been chosen as Besiktas’ new manager.
The 49-year-old has joined the Turkish club on a two-year contract that will expire in the summer of 2026, with the option to extend it by another year.
The former left-back has not played since his dismissal by the Ibrox club in November 2022.
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