The company will begin looking for a new CEO “very shortly”, Billingham told the PMA's sister title M&C Report, following Punch’s £2.3bn debt restructure expected next month.
The restructure now requires approval from just the Royal Bank of Scotland and Lloyds Bank after bondholders and shareholders voted in favour.
Griffiths has previously been linked to the chief executive role and asked if he is a candidate, Billingham said: “Yes he is. If he wants to be a candidate, he’s a strong candidate.”
Billingham, who expects to revert to a non-executive chairman role at the CEO’s appointment, added: “It needs to be somebody who is in retail, who is familiar with the consumer-facing aspects of the job. We won't just look in the pub sector, we’ll look outside that.”
He said he was “open minded” about candidates’ specific industries but said experience of franchising would be beneficial.
Billingham said he’d be looking for “evolution rather than revolution” under the new CEO and expects it to be “business as usual” after the restructure.
Asked if he’s confident the Royal Bank of Scotland and Lloyds Bank, which provide liquidity and hedging facilities to the two Punch securitisations, would approve the restructure, Billingham said: “I certainly hope so. The biggest hurdles we’ve got through were the bondholder and shareholder votes. All of those have gone though with very high percentages in favour.”