Melbourne's Grundy is now expected to move to Sydney after reportedly rejecting Port's advances.
Sweet, who has played 11 AFL games in two seasons but is off contract, covets more game-time but is second-choice ruck at the Bulldogs behind star man Tim English.
"The club was keen to retain Jordon having had a contract on the table for the majority of the year however the ruckman has a desire to return to his home state," the Dogs said in a statement on Tuesday.
"The club will now work with Port Adelaide to facilitate a suitable trade."
The looming Sweet deal comes as Grundy weighs his future at Melbourne, where his first season since transferring from Collingwood has failed to succeed in tandem with Demons skipper and ace ruckman Max Gawn.
Grundy is now set to join the Swans, whose lead ruckman Tom Hickey has retired.
And Port's desire to recruit Sweet could also spell the end of Scott Lycett's time at Alberton - the 30-year-old managed only four games last season and 13 so far this year amid frequent injury battles.
Lycett's contract will soon end at Port, who are in the box seat to sign defenders Esava Ratugolea from Geelong and Brandon Zerk-Thatcher from Essendon.
Both Ratugolea and Zerk-Thatcher are understood to have nominated Port as their preferred destination for next season.
The AFL's trade nine-day period officially begins on October 9.
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