Blair is the final player offered fresh terms this summer after reaching the end of his deal.
Boss Darren Moore revealed that, for now at least and with Rovers’ blessing, the 31-year-old will not be signing the offered contract and will assess other opportunities which may come his way in the next few weeks.
But he said the deal - which is a one-year deal with the option for a further 12 months - will remain on the table for Blair should he wish to return.
“At the moment Matty has not signed but he’s considered it,” Moore told the Free Press.
“I could get a phonecall at any time to say he has come back to us.
“What he is doing is thinking about the offer and opportunity and where he is.
“He lives down towards Coventry and he’s just checking things out.
“We’re hopeful that it can go for us.
“But I understand in Matty’s case, he’s probably looking for a longer term contract.
“He’s probably looking for a more concrete two years straight up.”
Blair was offered reduced terms as the club reacted to the financial implications of the Covid-19 pandemic and its impact on football.
He made 12 appearances for Rovers in an injury hit and curtailed season, taking his total number of appearances to 162 over four years.