The 29-year-old has been attracting admiring glances from overseas in recent weeks after enjoying another successful season with the Glasgow giants both domestically and in Europe.
What is the latest news involving Barisic?
A recent report from the Daily Record claimed that Turkish champions Trabzonspor and an unnamed Italian side are showing interest in Barisic.
Trabzonspor were crowned Super Lig champions for the first time since 1984 last season but left-back is a problem area with Tymoteusz Puchacz returning to Union Berlin after a successful loan spell.
Fode Ballo-Toure of AC Milan is also believed to be on their radar, though, and Barisic is said to be prioritising extending his stay with Rangers at this moment in time.
However, the Croatia international refused to rule out a possible exit in a recent interview while away with the national team, claiming ‘you never know’ in football.
“I don’t know only about the club, but I am good there and enjoy it,” said Barisic to RTL. “However, in football, you never know, there are always some inquiries.
“There could be an offer that satisfies the club and me. Of course, you will leave (then), but until then, it does not go further.”
What has O’Rourke said about Barisic?
It could be a summer of upheaval for Rangers, with the likes of Alfredo Morelos, Joe Aribo and Ryan Kent all approaching the final 12 months of their current contracts.
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And O’Rourke believes Barisic is another player who would carefully consider seeking a new challenge following a fruitful four years with the Gers.
He told GiveMeSport: “I’m sure the player would definitely give it a big consideration to move on as well. So maybe this summer could be the time that Barisic does secure that move away from Ibrox.”
Who could Rangers replace him with?
Barisic, who earns £18,000-per-week, will be a difficult player to replace, should he move on this summer, but it seems as though Rangers are already lining someone up.
The Scottish Sun state that manager Giovanni van Bronckhorst has placed Stoke City’s Josh Tymon on his wish list.
It’s said that the 23-year-old has a price tag of around £5 million, a figure that Rangers may not be able to afford until late on in the window when they’ve either sold players or potentially qualified for the Champions League group stages.