The Foundation of Hearts fans' group is competing with two rival parties to buy the Scottish Premiership club - one involving former Livingston owner Angelo Massone and another a partnership between US investors and Scottish businessman Bob Jamieson.
The interested parties submitted bids earlier this month and were asked to provide evidence of their financial power by the end of this afternoon.
Jackson told STV: "I'd imagine that one or two could fall away - they produce some sort of proof of funding but we need to decide if that's strong enough for us.
"I can see us making a decision on one or two of the offers that come in after close of business today.
"We will need a couple of days to look at what we have but we may still have to go back to the interested parties to clarify one or two things.
"Hopefully we can move to preferred bidder status within a couple of weeks."