Back in 2010, Lewandowski was due to hold talks with Rovers, as the battle to sign him from Lech Poznan was on-going.
Borussia Dortmund ultimately secured a deal, and the rest is history as the Pole is now one of the hottest talents in world football, which was highlighted by his four-goal haul against Real Madrid on Wednesday in the UEFA Champions League semi-final first leg.
"It's true," the West Ham boss said.
"He was put forward to sign very strongly by our recruitment staff and unfortunately it was one that got knocked back.
"My distant memory isn't that great but I think (former Rovers chairman) John (Williams) 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, yes. He's probably worth 40million euros now."
Allardyce admits he rues missing the chance to work with him.
"I think about it every time I see him play. Last night I was thinking it again," the 58-year-old said.
"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."