The 24-year-old is out-of-contract in the summer at Fir Park, and is yet to agree a new deal.
Rangers are now lining up a move for Law as they are targeting a number of free transfers.
The Gers are under a transfer embargo until September 1st - meaning they cannot sign players until after that date - so any potential signings would need to be free agents as the transfer deadline will be closed.
They can offer terms of employment to players who are due to be out-of-contract, such as Law.
The former Rotherham ace has impressed north of the Border since joining Motherwell in 2011 and could now get the chance to move to Ibrox.
Rangers are being linked with a host of these types of deals, with Cammy Bell, Murray Davidson, Andy Halliday, Jon Daly and Chris Humphrey all believed to be in their sights.