Gaydamak wanted £70million but is now willing to sell the Premier League side, which has debts of £40million, for just half that price.
Pompey chairman Peter Storrie said: “If we do not get a new buyer by next season it does not bear thinking about.
“It has been a nightmare. From when Sacha told me he could not put any more money in and had to sell, we were really working on keeping the club going.
“We had £12.5m left to pay on transfer deals and had to sell players.”