Sky Sports is reporting - via Sky sources - that the former Celtic and Borussia Dortmund midfielder has been contacted by the Paisley side following Jack Ross and James Fowler taking the reins at Sunderland.
Lambert won the Scottish Cup with St Mirren as a 17-year-old in 1987, and went on to play more than 200 games for the Buddies.
He was in charge at Stoke City but left when the Potters were relegated to the Championship.
The 48-year-old has had spells managing Livingston, Wycombe, Colchester, Norwich, Aston Villa, Blackburn and Wolves.
Former captain Jim Goodwin, currently in charge at Alloa Athletic; Livingston boss David Hopkin and ex-Hearts and MK Dons manager Robbie Neilson are also understood to be among the candidates for the job.