Hearts have offered goalkeeper Craig Gordon a two-year deal to return to the club.
The out-of-contract 37-year-old has an offer to remain with Celtic, but on much reduced terms.
St Mirren have previously spoken to Gordon about signing, and he wants assurances about playing regularly.
He has not played for Celtic since December, and did not feature in the league last season.
Gordon began his career with Hearts, making 100 appearances for the club before signing for Sunderland in 2007.
During that spell he played alongside Robbie Neilson, who was appointed as Hearts head coach for the second time on Sunday.