The former Sunderland boss has emerged as Newcastle's top target as they seek to replace the position left by Rafael Benitez at the end of last month.
Aston Villa Manager Steve Bruce during the EFL Sky Bet Championship match between Blackburn Rovers and Aston Villa at Ewood Park, Blackburn, England on 15 September 2018.
"I was certainly extremely surprised", Allardyce told talkSPORT about the approach. I politely said "no". I never got to talk to Mike [Ashley, owner of the club]. My agent contacted me, I had a think about it and a quick look at the situation and thanked them very much but (it's) not for me.
They also reported that if he had gone back to Newcastle, then his former player Kevin Nolan would have been assistant manager.
Newcastle hope to iron out the remaining details as quickly as possible and will endeavour to ensure Bruce is able to meet the players for the first time in China next week.
"I appreciated the offer but I was surprised".More news: Denise Nickerson Of 'Willy Wonka' Life Support Turned Off
More news: Williamson hails ´brilliant´ New Zealand after World Cup stunner
More news: Iran's Zarif calls on UK to immediately release captured oil tanker
"I had a think about it, but it wasn't something I thought about too long".
"I just thought it would be better for everybody if I made a quick decision because they are there in pre-season - I would have had to have been there in a day!"
Benitez departed after his contract expired, saying the Premier League club "did not share his vision".
The former Magpies manager claimed Sheffield Wednesday fans should be anxious about their team losing their manager as he thinks Bruce would jump at the chance to succeed Benitez if his current club doesn't stand in his way.
The 58-year-old is keen on managing in the Premier League again and wants to hear what Newcastle have to offer to him.