The 33-year-old was brought to Firhill in January after he was allowed to leave St Mirren and played a key part in helping the Jags retain their top-flight status.
But SportTimes understands Mair has been told he has no future at the club and will not be offered an extension to the short-term deal.
Mair featured 17 times in the second half of the campaign after he fell well down the Buddies pecking order.
He scored the third goal in last week's 4-2 win over Hearts that secured the Firhill side's place in the Premiership, but will now not be kept on as Archibald looks for another central defender to add to current options Conrad Balatoni, Gabriel Piccolo and Aaron Muirhead.
Thistle are set to lose left-back Aaron Taylor-Sinclair as he considers his future ahead of a Bosman switch this summer.
Forwards Steven Lawless and Christie Elliott are also out of contract this summer, but it's understood Archibald will look to retain both of them.
Lawless was the subject of a bid from Dutch side Willem II last summer, but has struggled to make the same impact he did during the Jags' First Division title-winning campaign and has held off penning a new deal.
Elliott netted three times for Archibald's side this term and is set to be offered fresh terms to keep him at Firhill.
Caolan McAleer, who spent last season on loan at Airdrieonians, has also not been offered a new deal.