He's previously been called up to the Argentina squad but has yet to receive a full cap. He believes moving to Europe will help him achieve this ambition.
The 25-year-old holds an Italian passport and would therefore not require a work permit as things currently stand.
Rangers are putting together a contingency plan in case Tavernier moves down south in the next transfer window.
The right-back was reportedly the target of Newcastle United though the English transfer window closed without Tavernier moving away from Ibrox.