Telford-born Bennett, 32, is out of contract at Ewood Park in the summer and understood to be available as the Championship side trim their squad.
Bennett could arrive on loan as the latest boost for Shrewsbury in a series of impressive January additions.
Midfielder Bennett, who was on the bench on his return from injury as Blackburn saw off Luton 1-0 today, has made just one appearance this season having been sidelined with ankle ligament damage.
The former Wolves academy graduate has spent five years at the Lancashire club, making 184 appearances in total. He previously spent a loan spell at Bristol City under Steve Cotterill in the 2015/16 season.
It is believed Bennett, who has made more than 400 league appearances across a 13-year career, would be keen to move closer to his Shropshire roots at this stage in his career.
Bennett, an Ewood Park team-mate of Shrewsbury's Peterborough match-winner Harry Chapman, made his return to Rovers' matchday squad for their victory today. He is the older brother of fellow football Kyle Bennett, who is at Bristol Rovers.
The former Bury, Norwich and Brighton man could also feature at right wing-back for Town, who lost loanee Matt Millar earlier this month.
A deal is likely to be struck before Monday night’s deadline, or revisited in the summer where the experienced Rovers man would be a free agent.
Town remain in the market for a centre-forward, while exits could also be possible before the deadline.
Cotterill has already boosted his midfield ranks this month after handing a short-term deal to David Davis, who has been unable to make his debut yet due to completing a period of self isolation.
Stand-in boss Aaron Wilbraham said after today’s excellent 2-0 victory over Peterborough: "When it gets to this stage with a couple of days left, you are always anticipating things."
Head of recruitment Keith Burt has been working on deals with absent boss Cotterill and chief executive Brian Caldwell.