Indian businessman Saurin Shah is believed to have held further talks this week with regard to his interest in purchasing the club from the Walker Trust and the Rovers boss wants the situation sorted as soon as possible.
The Lancashire Telegraph says Mumbai-based Mr Shah arrived in England with his consortium earlier this week as they continue their pursuit of Rovers, having already been believed to have offered in the region of £25million for the club.
Allardyce said: "I think, like everything else, it is speculation at the moment.
"There seems to be other interest as well as that one and from my point of view it would be very important to get the club sorted before we start a new season.
"It is a very difficult situation to deal with because you are not sure if and when a new owner is going to come in. And that can cause a little bit of uncertainty - certainly from my point of view because I have experienced that uncertainty before.
"I was at Newcastle and fell foul to a takeover by losing my job. If the club are to be sold then I would prefer it would be sold as quickly as possible."