New Wolves boss Dean Saunders is keen to bolster his squad having replaced Stale Solbakken at Molineux and defensive reinforcements are thought to be among his top priorities.
Wolves have struggled defensively this season and have conceded 38 goals in 26 games to leave them in 18th spot in the Championship.
Webster is thought to be among Saunders' targets as he looks to shore up Wolves' leaky rearguard during this month's transfer window.
Webster has impressed in his second spell at Hearts, regaining his place back in the Scotland squad after a number of impressive performances at Tynecastle.
Hearts are keen to keep hold of Webster, who is out of contract at the end of the season, but they could be forced to cash in on him due to their ongoing financial problems.