The 42-year-old five-time world champion is the highest-ranked player left in the tournament, which has seen holder Mark Selby, Judd Trump and Ding Junhui all fail to progress.
Despite his confident form, O'Sullivan, who had opened up a 3-1 interval lead over Welshman White with breaks of 132 and 64 before closing out a comfortable victory, suggested he might not be around to defend the title next year should he go all the way at the Barbican Centre.
Speaking in a post-match interview on BBC Two, O'Sullivan was asked if he was serious about following the likes of Steve Davis and Jimmy White as a participant on the ITV reality show, even if it meant not being able to play at the 2018 UK Championship.
He said: "I would, a million per cent, I'd do anything now, I would love it.
"I'm up for it. I used to think 'no, I couldn't do that, I've got to be a pure snooker player,' but you get to a stage when you think 'this is painful and that's all fun, a good laugh'.
"Everything I do away from snooker is great. I want to do that as much as I can, but also obviously want to play a bit of snooker do myself justice.
"As long as I am in the top 64, being number one, number 64, doesn't matter any more."
O'Sullivan added: "Why not? Let's have a bit of the jungle. They'll think I'm a gorilla when they look at me and I take my T-shirt off.
"I couldn't have done that trial last night, though, with the snakes. I'm gonna get trained for it, get used to the snakes."
O'Sullivan has often found himself embroiled in controversial issues, but the world number four intends to take things very much in his stride and let others worry about the future direction of the sport.
He said on BBC Two: "I tried to kind of get players together and do something, but they all just bottled out in the end, so I thought 'you know, I have just got to do my own thing, live my own life'.
"I have gone and done other bits outside snooker, because I can. This is a Brucie Bonus for me.
"I understand what the players are going through, but until they get their bottle together and stand up together, then they are just going to have to keep moaning.
"I got fed up with moaning, so I just thought I might as well go and get a good life, I have got a great life now, and I don't care what they do - they can play outside if they like in the freezing cold, I wont ever complain about a ref or an official, they are all fantastic."
O'Sullivan added: "I was ingrained in snooker, that was all I had done, so every little thing bothers you. It was frustrating, you want to get things sorted and the players to stick together, but they never do, so I thought 'you know what, get on with it."
Next for O'Sullivan is a clash with improving Thai youngster Akani Songsermsawad, who thumped Barry Hawkins 6-0 despite registering a high break of just 59, which he'll surely need to better to produce an even bigger upset later in the week.
Elsewhere in Tuesday's afternoon session, Neil Robertson, the world number 10 from Australia, was edged out 6-5 by Mark Joyce.
Scotland's John Higgins, the world number five, held off a recovery from Yan Bingtao of China to progress 6-3, while Mark King knocked out Belgian world number 13 Luca Brecel by the same scoreline to move into the last 16.
Martin Gould also advanced, beating Hossein Vafaei 6-4.
In the evening, Shaun Murphy beat Jimmy Robertson 6-3 to set up a clash with Ricky Walden, who was a 6-2 winner against Kyren Wilson.
Xiao Guodong beat Noppon Saengkham 6-3 to set up a clash with Gould.
Afternoon session
- Mark King 6-3 Luca Brecel (Match 103)
- Yan Bingtao 3-6 John Higgins (Match 104)
- Martin Gould 6-4 Hossein Vafaei (Match 111)
- Ronnie O'Sullivan 6-1 Michael White (Match 109)
Evening session
- Kyren Wilson 2-6 Ricky Walden (Match 102)
- Barry Hawkins 0-6 Akani Songsermsawad (Match 110)
- Shaun Murphy 6-3 Jimmy Robertson (Match 101)
- Xiao Guodong 6-3 Noppon Saengkham (Match 112)
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