Lappin parted ways with the club by mutual consent following six years at Carrow Road after struggling to establish himself in the first-team since their promotion to the Premier League last season.
The 29-year-old Scot spent time on loan at Cardiff during the first half of the campaign, making two appearances for the Championship leaders.
Mackay is now considering whether to sign the free agent, who made 126 senior appearances for Norwich after joining from St Mirren in 2007.
"He is certainly someone under consideration," Mackay told the Pink'Un.
"We are still thinking about what we are going to do in terms of defensive cover and we will make a judgement on that before the end of the month.
"He has been here recently and he is someone that can comfortably play in a Championship team.
"He was a smashing professional when he came here, a good boy and a good personality to have around."
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