The current West Ham boss had the chance to sign the Poland international in 2010 but was hindered by a lack of funds as well as a volcanic ash cloud that prevented negotiations
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, the forward eventually joining BVB instead.
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"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 (£33.6m) now," the Hammers boss added.
"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."