The Scottish international hasn’t played a single minute of action for Norwich City since the end of August and has only been named on the substitutes bench three times.
Rangers are looking to strengthen during the window as they look to close the gap on rivals Celtic at the top of the Ladbrokes Premiership.
They look set to be without Bruno Alves for the foreseeable future after the Portuguese international was pictured in a leg brace following an injury in the recent clash with Celtic, and Martin could act as the perfect short-term replacement.
Martin has been with Norwich City since 2010 and is still the official club captain despite his lack of playing time recently.
He is familiar with Rangers boss Graeme Murty from their time together at Carrow Road when Murty coached the under-16s and then under-18s between 2014 and 2016.