The 29-year-old prop has spoken to the Australian media following allegations of a lewd video chat involving Rabbitohs players.
Reports in Australia over the weekend claimed one of Burgess' social media accounts had been used to send inappropriate images to a woman following a match in May.
Speaking on Tuesday, Burgess said he could not go into any details publicly but hopes an NRL investigation will be finalised within the next 48 hours.
"There's an inquiry going on with the NRL and I'm happy for the truth to come out," Burgess told a press conference.
"I'm completely happy to go through the process, be as open and honest with everything and I'll follow that process and hopefully it will be resolved sooner rather than later.
"Whilst that process is taking place I can't talk about it publicly.
"I'm glad that I'm stood here today, I'm glad I have the chance to address it and speak to you guys (media) so you understand where I'm at.
"I'm not running away and hiding from what's out there."
The Rabbitohs face Sydney Roosters in the NRL preliminary final at Allianz Stadium on Saturday for a place in the Grand Final.
Burgess added: "It's a tricky time but it is what it is. We're all stood here, talking about something when really we should be focusing on the game that's coming up in a few days."
The former Bradford player and dual-code international, whose wife is heavily pregnant with their second child, added: "What hurts me the most is seeing my wife upset about what's out there.
"I've got a wife who loves me, I've got a great family, I've got great friends, great support around me that have obviously helped through these allegations that have been made.
"You do feel it but I've had certain experiences in my life before, had serious emotions I've had to deal with, and football has always been great for me."
South Sydney coach Anthony Seibold previously threatened to walk out of a press conference and refused to answer questions about the matter.
"We take the accusations seriously, as do the integrity unit. At the moment, they're accusations," Seibold said.
Burgess, who played for England in the 2015 Rugby Union World Cup during a brief switch of codes with Bath, recently signed a four-year extension to his contract which will keep him with the Sydney club until the end of 2023.
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