The Reds have been hit hard by injuries at centre-back, with Virgil van Dijk and Joe Gomez long-term absentees, and after Joel Matip limped off against Tottenham on Thursday, are looking for a short-term solution.
Mustafi is understood to be one option under consideration, with the German into the final six months of his contract at Arsenal.
No contact has been made with the Gunners yet, with Liverpool looking at a number of players before Monday’s deadline.
Mustafi is thought to be open to leaving Arsenal this month if the right offer presents itself in the coming days.
The 28-year-old has been attracting interest from other clubs, namely Lazio in Italy, but nothing concrete has emerged.
Mustafi has not played for Arsenal since Boxing Day and has only made three Premier League appearances this season.