The Bombers have reportedly offered a four-year deal worth as much as $800,000 per season.
If the Saints want to keep the 27-year-old they can match that offer, which would mean Goddard's only passage out of St Kilda would be via a trade or the draft.
While Goddard is yet to declare his hand, several players have already told their clubs they want to leave including West Coast's Quinten Lynch and Melbourne's 2011 best and fairest Brent Moloney.
Out-of-favour Carlton veterans Jordan Russell and Bret Thornton both intend to use their unrestricted status to find new clubs, as does Port Adelaide's Steven Salopek while Essendon forward Angus Monfries, Melbourne defender Jared Rivers and Geelong fringe player Shannon Byrnes are other potential movers.
Adelaide spearhead Kurt Tippett looks set to return to his home state Queensland but will have to wait until the trade period starts as he has not played long enough to be a free agent.October 19 is the deadline for players to field offers from rival clubs under free agency while the trade period runs from October 8-26.