Grigg, 29, almost became a Town player on deadline day last January but a loan move from Sunderland broke down in the final stages.
And the Shropshire Star understands reported interest in the centre-forward who cost Sunderland £4million two years ago is genuine, though Town are thought to face competition for his signature.
Boss Steve Cotterill, who is away from the club at the moment as he recovers from Covid-19, wants to build a side that can compete in League One.
And a striker of the calibre of 13-capped Northern Ireland hitman Grigg is on Shrewsbury’s radar as they aim to add more firepower to their ranks before Monday’s transfer deadline.
Birmingham-born Grigg has more than 100 career league goals since breaking through at Walsall in the 2010/11 campaign’ He has enjoyed prolific spells with the Saddlers, MK Dons and Wigan, as well as being involved in three promotions.
Sam Ricketts’ Shrews were close to sealing his signature in the final hours of the window last January. Ricketts said the striker was keen to join Town on loan from the Black Cats, where he has scored just eight goals in 57 outings amid injury problems.
Reports suggest Town’s League One rivals MK Dons are one of the sides also in for Grigg’s signature, as well as big-spending League Two side Salford, who have had a long-standing interest in the former Latics star.
Sunderland are thought to be looking to move on the big-earning striker, who has been struggling with a knee injury and has not featured since mid-December.
Grigg has 18 months left on his Stadium of Light deal. Town already have four strikers and Shaun Whalley on their books.