Chelsea terminated the midfielder’s contract on Monday and he is now available on a free transfer this summer.
His free agent status means that clubs can afford to wait until after deadline day on Thursday to snap the player up.
Rangers are interested in signing him and Barkley could be prepared to take a significant pay cut to move to Glasgow in the coming days.
But it has been claimed that there is at least one Premier League club who are interested in him as well.
He remains a coveted talent in the Premier League despite his underwhelming years at Chelsea since his move from Everton.
But Barkley has the option of staying in the Premier League if the unnamed club table a concrete offer.
However, Rangers being in the Champions League is a big draw for the player as well, who wants to play in Europe’s elite competition.
The Glasgow giants believe that the lure of playing in the Champions League could help them land the midfielder this summer.
