Former Wasps player Ken Moss agreed to buy the club in June but the confirmation of the deal was delayed due to financial issues.
However, Rigby has informed the club's fans that talks are nearing a conclusion and that an announcement will be made shortly.
The chairman told the club's website: "As communicated in recent months, terms were agreed on the sale earlier this summer but it is fair to say that there have been some complex financial issues to resolve since that time which has prolonged the process much longer than anyone involved would have liked; but such is the nature of this transaction.
"I am pleased to say that we are nearing the end of the process now and we anticipate that we will complete imminently and a further statement will be issued at that time."
Wasps begin the new season by hosting Harlequins on Saturday afternoon.