Off-contract at the end of the season, Burgess is rumoured to be the target of an Eels side hopeful of beefing up their pack.
There was some suggestion on Wednesday a move might be expedited to round one of this year, with the Eels having a significant chunk of their salary cap still at their disposal.
But the Rabbitohs have put paid to the idea, insisting there has been no request for a release and Burgess won't be going anywhere.
"George Burgess is contracted to the South Sydney Rabbitohs until the end of the 2019 season and will be playing for (Souths) throughout the 2019 season," the club said in a statement.
"Neither George Burgess nor his management have requested a release from the remainder of his contract and George has indicated that he wants to play for the Rabbitohs in 2019."
George is the only Burgess brother not to have signed on long-term at the Rabbitohs, with Sam and Tom locked in until the end of 2023.
The 26-year-old has also been linked to Brisbane this off-season, with the English prop expected to test his value on the open market later this year.
He is arguably the best front-rower off contract next season, along with Melbourne's Christian Welch and Brisbane's Joe Ofahengaue.