Barisic, who shared the duties with Calvin Bassey at left-back last season, and still has two more years left on his current deal at Ibrox.
However, with the transfer window in full swing, the Croatian has popped up on the radar of several clubs across Europe.
Turkish outfit Trabzonspor, who are gearing up for a season in the Champions League, are keen on a move for Barisic, while he also has attracted interest from Italy.
But despite several clubs being keen on snapping up the Croatian international, Rangers have not had contact from any potential suitors.
Although Barisic is claimed to be a player in demand this summer, Rangers are yet to see any clubs confirming their interest in a move for him.
Trabzonspor could intensify their efforts to snare away Barisic, but they have so far not made any official approach.
The full-back is not guaranteed to remain at Ibrox beyond the ongoing window, but as it stands, there is no change in his contract situation at the club.
