Allardyce says it is "doubtful" that Indian businessman Ahsan Ali Syed will takeover the club.
Syed has been in talks to buy the Ewood Park outfit for £300m but BBC 5 live reported this week he has a trail of unpaid debt in the UK.
Allardyce said: "If it's happening, it's going to happen in the next week or two.
"Whether it does happen seems doubtful, for whatever reason I don't know. I'm not privy to that information."