But the Rabbitohs playing group has tipped the club legend to return in the future.
Burgess joined the Rabbitohs' coaching staff as an assistant in 2020, the season after a shoulder injury ended his 182-game NRL career.
As a player, the English national first made a name for himself with Super League outfit Bradford in the late 2000s.
But he went on to become synonymous with South Sydney, receiving the Clive Churchill Medal as player of the match in their drought-breaking 2014 grand-final victory.
He has since served as an assistant to current Souths boss Jason Demetriou and his predecessor Wayne Bennett.
As a head coach, Burgess led the Russell Crowe-backed Orara Valley Axemen to the grand final in last year's Group 2 rugby league competition.
Burgess informed the Rabbitohs playing group of his new job on Tuesday morning, but the team does not believe they have seen the last of the champion forward.
"If he's going over there and coaching in the Super League, then I don't see why he can't come back," said prop Jai Arrow.
"I'm sure the big fella wants to come back one day because it's probably too cold for him over there."
Cook, a teammate of Burgess for four seasons, believed it was inevitable the Englishman would be scouted for a head-coaching role.
"He was always destined to do that," Cook said.
"He must think that's the path to go, go overseas, get an opportunity and build some confidence but I think there's no doubt that he'll find his way back here as an assistant or a head coach at some stage.
"They'll love him over there."
Burgess insisted his focus remained on the Rabbitohs' 2023 premiership tilt but teased a possible return.
"We still have an opportunity to play some great football for the remainder of the year, and to do so alongside our current staff and squad is my focus," he said.
"This is not goodbye, but see you all soon."
Burgess has signed a two-year contract with Warrington, who sacked head coach Darryl Powell last month following a 42-6 loss to last-placed Wakefield Trinity.
Matt Dufty, Paul Vaughan and Sam Kasiano are among the ex-NRL players currently on the Wolves roster.
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