The 26-year-old previously revealed he had held initial talks with the Power and Crows in regards to potentially extending his 113-game career.
The Power will contemplate a selection for Dumont this week, with the National Draft and Rookie Draft two avenues that could see the South Australian call Alberton Oval home for 2022.
"We follow all South Australians in the system," Parker said, per AFL.com.
"We have spoken to Trent Dumont, but whether he does make it onto our list, and how that happens, depends how the draft plays out."
The Power currently hold Picks 12, 63, 73, 74 and 92 for the draft and could look to utilise one of their later selections to acquire Dumont should their planning skew towards the former Norwood representative.
The Rookie Draft will take place on Friday and could be a likely option for Dumont to join Port Adelaide for next season, while the Pre-Season Supplemental Selection Period - which will take place early next year - is a third option.
Dumont has flagged he would look to make a return to the Redlegs in 2022 should he see no avail in continuing his AFL career.
Port Adelaide are set to draft Jase Burgoyne, son of Peter, as a father-son selection at this week's National Draft.