Gers boss Giovanni van Bronckhorst is keen to strengthen his squad as he looks to wrestle the Scottish Premiership title back from rivals Celtic.
He is poised to work with a limited transfer budget though and will need to wheel and deal over the summer window.
Van Bronckhorst wants to add Stoke defender Tymon to the ranks, but the Potters want around £5m to let him move on.
It is suggested that in order to fund a swoop for Tymon, Rangers will need to either sell Barisic or reach the Champions League group stage.
Tymon, 23, came through the youth ranks at Hull City and joined Stoke in 2017.
Stoke loaned Tymon out to MK Dons and Portuguese side Famalicao earlier in his stint at the club to gain experience and he made 48 appearances for the Potters this term.
It remains to be seen if Rangers will have the funds needed to tempt the left-back to Scotland.
