Out-of-contract Geary, who turned 26 last month, is an unrestricted free agent.
He has not played for the Saints since Round 7 when he injured elbow during his 100th AFL match.
And there is speculation the Cats are considering offering the tough defender a lucrative deal to lure him down the highway.
Geary's manager, Anthony McConville, was tight lipped when contacted by Sportal.com.au.
He refused to say whether Geary was committed to staying at St Kilda, which drafted him as a rookie in 2007.
Geary injured his elbow against Hawthorn at the MCG in Round 7. Photo: Getty
From country Victoria, Geary would add depth to Geelong's half-back line as the Cats look to keep their premiership window open.
He'd be the ideal replacement for 32-year-old veteran Corey Enright, and premiership teammate Joel Corey - who retired at the end of last season.
Geary has been floated as a potential St Kilda skipper once Nick Riewoldt retires.
Ben McEvoy had also been mooted as the next captain, before he was sent to Hawthorn in a shock trade last year.
Losing Geary would also deepen the club's list problems.
The Saints only had eight players aged between 25 and 28 at the start of the season, and Geary was one of those.
Brendon Goddard (Essendon) and Nick Dal Santo (North Melbourne) are other Saints to leave the club via free agency.