Rovers were in talks with the Poland international in the summer of 2010 but the club's financial state - as well as the volcanic ash cloud that meant that all flights in and out of the UK had to be suspended - scuppered the move, with the forward eventually joining BVB instead.
With Lewandowski having gone on to score 74 goals since – including all four in his side's 4-1 Champions League semifinal win against Real Madrid on Wednesday – Allardyce admits that he is always reminded of the near-miss every time that he sees the striker play.
"I think about it every time I see him play," Allardyce told reporters. "My distant memory isn't that great, but I think John Williams [former Rovers chairman] and the board said we are not going to commit that amount of money.
"I think they wanted three or four million euros, but we were particularly strapped financially at the time at Blackburn.
"I watched him play but I didn't get the chance to meet him. I think his agent said he couldn't come over because of the ash cloud.
"He's probably worth 40 million euros now."
"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."