With Ianis Hagi sidelined for an extended period owing to a knee injury, Rangers boss Giovanni van Bronckhorst has been looking to bring in a new attacking midfielder this summer.
The Gers zeroed in on Bayern Munich man Tillman as their top target and have been in talks with the Germans over a deal for him.
Rangers made headway in their negotiations to snap up the American from the German giants and are now closing in on a loan deal for him.
Tillman will initially arrive at Ibrox on a temporary basis for the upcoming season but Rangers will have the option to make his transfer permanent next summer
But according to German magazine Kicker, Bayern Munich have secured a buy-back clause in the deal to send Tillman to Rangers on loan.
If Rangers do sign the midfielder permanently next summer, the Bavarians will still have the option to take him back to Germany for a fixed price.
Bayern Munich will therefore retain control over the player’s future, should they trigger the clause.
As it stands, Tillman is contracted at the Allianz Arena until the summer of 2024, but he could find himself leaving the club prematurely should he manage to impress while on loan in Scotland.