The 28-year-old is out of contract with the Scottish Championship side at the end of the season.
The midfielder is out of contract at Ibrox at the end of the season, and The Scottish Sun claims that talks over a fresh deal have yet to begin despite the player wanting to remain with Mark Warburton's side.
Doubt regarding the 28-year-old's future has seen his former club join the race to bag his signature. Law came through the youth system at Bramall Lane but only made five league appearances for the Blades - spending most of his time out on loan - before departing for Rotherham in 2009.
Despite it appearing that Law will be leaving the Scottish Championship side at the end of the season, Warburton has been happy to call upon the midfielder this term. He has made 18 league appearances for the Gers with 10 starts, and came off the bench to play the last 25 minutes of normal time as well as extra-time of the Light Blues' Scottish Cup semi-final with Celtic, before scoring what would ultimately prove to be the winning penalty.
Nevertheless, with Rangers heading up to the top flight next season, and with the likes of Josh Windass and Matt Crooks coming in to bolster the midfield options, it seems likely that if Law stayed, he would find opportunities extremely limited.