Indian businessman Saurin Shah is interested in taking over from the Walker Trust at Ewood Park but no deal has yet been agreed.
Allardyce claims the continuing uncertainty is stopping him from bolstering his squad and he wants the issue resolving quickly.
The Blackburn boss, whose side lost 1-0 in a friendly at Huddersfield on Wednesday, said in The Sun: "We need to know what is happening sooner rather than later.
"I know there is all the due diligence business to go through, but surely you either want to buy a football club or you don't. It is as simple as that.
"While it is dragging on, it means we are financially restricted and it is stopping me enhancing my side for the new season.
"I don't even know what the prospective new owners would be bringing to the table anyway.
"I am looking for a striker who can challenge Jason Roberts and Niko Kalinic, but going for someone like that is extremely difficult at the moment.
"When you have not got as much money as everyone else, it makes it difficult to find the right player."