Petracca, the Norm Smith medallist in the Demons' breakthrough 2021 flag and the face of the club, wants to become a Suns player despite having four years left on his contract with Melbourne.
St Kilda lodged paperwork to recruit free agents 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 captain Zach Merrett are among the big names who could be on the move in the trade period, which begins on Monday and runs until October 15.
The Suns, currently boasting draft picks six, 14 and 17, will need to give the Demons a deal juicy enough to entice them to release Petracca.
Melbourne are also among the clubs keen on Gold Coast's Sam Flanders, and are reportedly chasing fellow Suns midfielder Bailey Humphrey, who is contracted to 2028.
Carlton and Collingwood are also among the Victorian clubs keen on Humphrey.
Petracca, who would add a dynamic element to a Suns midfield led by Brownlow Medal winner 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 this week.
It signals an era of change for the Demons, who have told 2021 premiership stars Clayton Oliver and Steven May to look for other clubs, and could also lose young defender Judd McVee, who wants a move home to Western Australia.
The free agency period, which runs until October 10, started on Friday, with Carlton receiving an end-of-first-round pick (currently No.20) as compensation for losing unrestricted free agent Silvagni to St Kilda.
The Blues also opted not to match the Saints' monster eight-year offer to restricted free agent De Koning, receiving a first-round draft selection (currently No.9 overall) as compensation.
Hawthorn elected not to match Geelong's four-year offer to restricted free agent James Worpel and received an end-of-second-round pick (currently No.40 overall) as compensation for losing the star midfielder.
In other free agency moves, 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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