The ex-Albion man, who signed for Wolves after spells with Watford and West Ham, was out of contract in the summer after two and a half seasons at Molineux.
Throughout the transfer window he has been linked with various Championship outfits.
He was strongly linked with Wrexham before they signed former Wolves skipper Conor Coady.
But despite the transfer window slamming shut - it looks like Dawson could be close to landing a new club.
According to reports, Blackburn Rovers are keen to bring in Dawson on a free transfer after a number of their key defenders departed in the window.
It would see the former Albion defender sign for an ex-Baggies manager in Valerien Ismael - although the two did not work together at The Hawthorns.
A move would see Dawson featuring for the seventh club of his career - having emerged from the youth system at Rochdale.
Albion plucked him from the lower league club and he went on to feature over 200 times for Albion - before departing for Watford.
He then went on loan to West Ham before making the switch permanent - and in January 2023 he penned a two and a half year deal at Wolves.