The Premier League side's Carling Cup tie against Peterborough United will go ahead as planned on Tuesday but it is has been suggested that there are five cases at the club in total.
"We've had one more case this morning, one more player and there are a couple of staff," confirmed Allardyce.
David Dunn and Chris Samba missed Blackburn's 5-0 defeat at Chelsea on Saturday but, when asked whether they were two of the players suffering from swine flu, Allardyce added: "It's definitely swine flu - you've speculated on the names and I'll leave it at that.
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"The Premier League has tried to sit on the fence by saying that we didn't request to have the game called off.
"We knew we couldn't get the game called off because we were told way back in February or March when we took some guidelines that unless there was some government legislation, everybody had to do whatever they had to do.
"If there was a swine flu outbreak, you couldn't call a game off, no matter what.
"We fulfilled our responsibility by confirming two cases of swine flu and suggesting that it looks like one or two other players and members of staff had similar symptoms - and we made the same phone call to Chelsea.
"It's a highly contagious strain as everybody knows but I can't comment any further than that."