Craig Gordon could be in line for a return to Tynecastle.
The 37-year-old, who made 176 appearances in his first spell at the club, struggled for games at Celtic last season following the return of Fraser Forster on loan from Southampton.
With Robbie Neilson's appointment as Hearts boss confirmed on Sunday, Gordon is reported to be considering a move that would reunite him with his former team-mate.
SunSport reports that Gordon is considering a two-year deal offered by Hearts after rejecting a move to St Mirren.
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The report says that Celtic boss Neil Lennon is keen to hold on to Gordon as backup for Forster, but Gordon rejected Celtic's first offer and is unimpressed with how negotiations with the club have unfolded.
They say that the club would discuss a potential testimonial match and support Gordon as he starts his coaching badges, with a 12-month extension also a possibility at the end of the two-year deal.
Gordon left Tynecastle in August 2007, with the £9m paid by Sunderland at that time the biggest fee spent on a keeper by a British club.
