Dundee defender Mair is already in talks with the Division Two side as they look to bring in some defensive reinforcements in the summer months.
"We are talking to Lee Mair," stated McIllroy to the Manchester Evening News.
"Danny Griffin is out until September and it is important to get some cover at the back."
Meanwhile, Bournemouth front-man Feeney (pictured) is also a top target for the former Northern Ireland boss as he looks to boost the firepower he has at his disposal.
"We are pursuing Warren Feeney," the Stockport chief said. "Bournemouth are haggling over the fee, but the move has been agreed with the lad in principle."
