The 69-year-old spent time with the Seasiders during the early stages of his coaching career, overseeing things at Bloomfield Road between 1994 and 1996.
He went on to make a name for himself with Bolton Wanderers, before adding the likes of Newcastle United, Blackburn Rovers, England and Everton to his CV.
Allardyce’s most-recent job came with Leeds United last year – which ended with the Yorkshire club being relegated from the Premier League.
The former Preston North End defender has now hinted he would be open to taking over the vacant Wales job left by Page- who was sacked last week following three-and-a-half years in charge.
“I’ve had quite a few Welsh coaches and know them quite well, you never know if you get on the shortlist for an interview,” Allardyce said on No Tippy Tappy Football.
“I’d always take an interview, I wouldn’t turn an interview down, you’ve got a team that’s done brilliantly over the last few years but who are the next generation, where’s the next Gareth Bale, teams like that always have to have one special player.
“With other countries they have one special player that can actually make the expectations for the nation greater than what they think because they can win a game any time.”
Allardyce is currently third-favourite on Sky Bet at 8/1, with Craig Bellamy (3/1) and Osian Roberts (11/8) both ahead of him.
Meanwhile, Mark Hughes and Thierry Henry make up the top five, with both at 10/1.