Allardyce, who was then the boss of Blackburn Rovers, was due to hold talks with the Polish forward in 2010 but the move never materialised, and the former Rovers chief believes that the 24-year-old would have been a hit in the Premier League.
The 58-year-old told reporters: "I think about it every time I see him play. On Wednesday night, I was thinking it again. He would have had a period of getting used to the level and the physical presence, but with a talent like that it wouldn't have been too long before he started to shine and score goals.
"The level he is playing at now is unbelievable, not just his scoring ability but his ability to retain possession.
"There were a lot of people looking at him at that time as well but we had the edge over everyone else because of the attraction of the Premier League. He could have used us as a stepping stone but it didn't happen."
Lewandowski has been linked with a move to Manchester United in the summer.