Petracca, the Norm Smith medallist in Melbourne's breakthrough 2021 flag and the face of the club, wants to become a Sun despite having four years left on his current contract.
St Kilda lodged free agency paperwork to recruit Tom De Koning and Jack Silvagni on Friday then revealed Steele has stepped down as captain.
"Jack (Steele) advised the club he wants to stay but is prepared to consider opportunities if presented," the Saints said in a statement.
Petracca, Steele, Carlton spearhead Charlie Curnow and Essendon skipper Zach Merrett are among the big names who could be on the move in trade period, which begins on Monday and runs until October 15.
The Suns, boasting picks No.6, No.13 and No.16 in their current haul, will need to give the Demons a deal juicy enough to encourage them to release Petracca.
Melbourne are also notably among the clubs keen on Suns midfielder Sam Flanders.
Petracca, who would add a dynamic element to a Suns midfield led by Matt Rowell and Noah Anderson, agitated to leave Melbourne last year but ultimately didn't request a trade.
Gold Coast appeared the only team in the running when Adelaide reportedly withdrew from the race for Petracca, having met with him last week.
It signals an era of change for the Demons, who have told midfielder Clayton Oliver and defender Steven May to look for another club.
The free agency period, which runs until October 10, kicked off Friday with Silvagni shifting from Carlton to St Kilda as an unrestricted free agent.
The Blues were given an end-of-first-round selection, currently pick No.19, as compensation for the defender's exit.
Carlton are not expected to exercise their right to match St Kilda's monster eight-year contract offer to restricted free agent De Koning.
In other free agency moves, Hawthorn will have three days to assess and decide whether to match Geelong's four-year offer to star midfielder James Worpel, who is a restricted free agent.
Melbourne premiership player Charlie Spargo (North Melbourne) and GWS defender Jacob Wehr (Port Adelaide) have officially found new clubs as unrestricted free agents.
Back-to-back premiers Brisbane are set to strengthen their list with the addition of Essendon ruckman Sam Draper and West Coast forward Oscar Allen.
Collingwood forward Brody Mihocek is weighing interest from Melbourne, while Gold Coast midfielder Brayden Fiorini has a choice between Essendon, Port Adelaide and the Suns.
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