In an interview, Metropoulos, the 69-year-old turnaround artist, swatted back rumours, saying "it was too early to consider a sale or IPO at this time."
The ubiquitous, legendary brand on which they had pledged millions in repairs, he said, still had plenty of room to climb.
"We feel that we're just two years into this wonderful turnaround of this company, and that there's a lot of potential growth to consider."
Its sales have yet to recover to the nearly $1 billion a year it reached before the bankruptcy.
But by following a turnaround playbook refined by Metropoulos - slashing jobs and costs, investing in automation, spending wildly on marketing campaigns that dubbed Twinkies' return "The Sweetest Comeback in the History of Ever" - the company has arisen from the ashes to regain a place in American pantries - and ensure another hyper-profitable flip for its deep-pocketed rescue team.
Metropoulos said over the past few weeks he had received "a number of calls" to buy the company, and fielded a proposal from bankers over a potential Hostess stock-market debut.
He would not offer details on how much they could raise in an IPO. Apollo spokesperson Charles Zehren declined to comment.
Metropoulos' mega-deals have tended to focus on troubled but well-known household names that he can buy for cheap, reinvigorate for a few years, then sell with a newly hyped turnaround story, to a long-term operator or highest bidder.
But the billionaire would set no timeline for when he expected to flip the company, saying only that corporate leaders would "continue to focus this coming year on expanding the business," and adding, "It's hard to call when we will consider something".
In two years, Metropoulos said, the leaders have invested more than $150 million in "improvements and efficiencies" at the firm's bakery plants, and spent hundreds of millions on marketing to remind hungry buyers the snack cakes were ready to buy and unwrap.
The cakes' revival was fuelled by the free hype of national sweet-tooth nostalgia, as social media lit up with tweeted cravings and celebrations of their sweet return.