The frontmen reunited with bassist Alan Lancaster and drummer John Coghlan to make their movie "Hello Quo" which resulted in the announcement of four UK shows in 2013.
With most of those all but sold out, and a pre-sale taking just ten minutes to fill up, more dates have been added to the run and the pair admit they've turned their thoughts to traveling further afield.
Speaking at Classic Rock's eighth annual Roll of Honour awards ceremony in London on Tuesday, Parfitt said: "Of course, it was great news to hear. Nobody knows what to expect in the future, but if the gigs are as successful as we're hoping then, dare I say it..."
Rossi said: "Dare! Dare!"
Parfitt continued: "There could be a world tour in 2013."
They said there had been discussion about dates in Australia and Germany but nothing has been decided as the band are wary of taking too many risks.
"It's not just about whether or not we want to do it," Rossi said. "The business reasons have to work."
But Parfitt added: "If none of us dies in the meantime, that could well be on the agenda."
He previously reported that Quo intend to use their 1977 live record as the template for the Frantic Four shows. The band won the Classic Album award on Tuesday for the double-disc release, recorded at the Glasgow Apollo.
The current Status Quo lineup are currently touring in Europe, with the show arriving in the UK for ten dates starting on December 6.
Status Quo Frantic Four shows 2013:
03/6: Manchester Apollo 03/7: Wolverhampton Civic 03/9: Glasgow 02 Academy 03/10: Glasgow 02 Academy 03/12: Manchester 02 Apollo 03/13: Wolverhampton Civic 03/15: London, Hammersmith Apollo 03/16: London, Hammersmith Apollo 03/17: London, Wembley Arena