O’Sullivan caused a stir at the UK Championship in York on Sunday when he mooted the idea of a breakaway circuit as a result of frustrations about the way parts of the game is being run.
The five-time world champion, who turns 43 on Wednesday, said he was “ready to go” and form a Champions League-style event of his own if he could find enough players to go with him.
World Snooker boss Barry Hearn called it a “cranky scheme” on Monday, while Judd Trump said his rival was “living on a different planet”.
O’Sullivan rowed back a little on Monday, saying he preferred to remain on World Snooker’s tour but wants “tweaks” to things, such as a schedule fairer on leading players and a different way of allocating ranking points.
“As the biggest draw in the game, what he says counts and it matters to the public, the players and World Snooker. Ronnie could be such a power for good in snooker if he wanted to be,” said Murphy, who leads the Players Commission.
“I know he’s been invited to get involved with the Players Commission, he’s welcome to come to any meeting the WPBSA has and I know the powers that be at World Snooker are keen to speak to him as well.
“We value his input and we’d love for him to get round a table and come at us with some really good ideas. It’d be good to get them down on a bit of paper and discuss them professionally.”
Seven-time world champion Stephen Hendry, retired since 2012, was a player O’Sullivan said would possibly star on notional tour.
“Ronnie mentioned to me the other day if there were any invitation events would I fancy playing,” the Scot told the BBC.
“I said ‘absolutely’. I already play on the Senior Tour so it’s not like I don’t play and I just said ‘yeah, absolutely’.
“I had no idea about everything that was going to happen after it!”
Tuesday’s afternoon session at The Barbican saw Stuart Bingham hit a tournament highest break of 145 in the opening frame of his 6-2 win over David Gilbert, following up with two more century clearances.
World number five Judd Trump beat Mark King 6-2 in their third-round match, while Australian Neil Robertson edged out Scotland’s Graeme Dott 6-5.
Marco Fu’s hopes ended with a 6-3 defeat by Jack Lisowski.
The Gloucester left-hander, 27, was pleased with the win which set up a last-16 meeting with O’Sullivan this afternoon, which could also lead to an appearance at the Masters.
“It could be a cracking match against Ronnie, I think we are the second and third-fastest players on tour,” said Lisowski.
“I hope I can keep up with him and score. The way I play, if I go for my shots and have a really good day then 99 per cent of the time I will win because I can be hard to play against. But Ronnie is the same and a real handful as we all know.
My recent consistency is still all new to me and maybe I can start to believe I will beat these top players. It will be a really good test to see where my game is at. Ronnie can blitz people and beat them 6-0 – but I have a chance if things go my way and he has an off day.
“I am trying to win every tournament I enter now, until it happens I won’t really believe it is possible. But I am very happy to be in the last 16 here, and have done a lot to help my Masters chances.”
In the evening session, Northern Ireland’s Mark Allen defeated Hossein Vafaei Ayouri 6-2, while Sheffield-based Ding Junhui kept alive his hopes of winning the title by beating compatriot Xiao Guodong 6-4.