The 62-year-old resigned from Crystal Palace in May, announcing he was leaving management after securing the South Londoners' Premier League safety.
Before that escape act, Allardyce had worked magic with Bolton Wanderers, Blackburn Rovers, West Ham United and Sunderland.
In almost 20 years of managing in England's top division, Allardyce never once experienced relegation.
"If another club say 'Can you come and save us?', I don’t think that’s for me now," he told talkSPORT radio on Wednesday. "I’ve been there and I’ve done it.
"If I had to consider anything now it would be an international position, but even that would have to be right for me and where I felt I would have a chance.
"When you are on international duty, it is all focussed on you, but of course after that months go by before you meet up again, so that would maybe suit me, if I am enticed back into the game."
Allardyce left his role as England manager by mutual consent in September 2016 following a newspaper sting after just 67 days and one game in charge.
He said he had accepted the Palace job in December to get over the subsequent depression.
"I was in shock for two or three weeks trying to get my head around what happened. I was in a daze, I was staring into the abyss," he said.
"I am very grateful to Crystal Palace - hugely, hugely grateful - because Crystal Palace was one of the things I felt I had to do to overcome the depression and the disappointment that I had suffered in the short spell I'd had with England.
"I had to get back to work and I had to get my teeth into another position to get over and move on, move forward, and life is very good at the moment."
Allardyce said he would spend time travelling around the world but recognised it would be hard not to stay involved in the sport.
"The problem for me will be to get through this season because of the itches that will certainly come around when the season starts. I'm definitely going to miss it, there’s no doubt about that," he said.
(Reporting by Alan Baldwin, editing by Christian Radnedge)
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