The Football League chairman indicated the body are becoming weary by the lack of progress at the League One outfit, who have twice entered administration since 2009.
A supporters group are attempting to take control of the stricken Fratton Park club, but Clarke admits time is running out.
"Portsmouth are at the last chance saloon. They can't enter another season in administration," Clarke said. "So they either sort themselves out before the start of next season or they are out of the Football League.
"The Football League has given them every opportunity and the administrators have given them every opportunity for the fans to buy the club - they are now the preferred bidder.
"They are going to the High Court. They are trying to get a deal which they can afford on the stadium so they'll have somewhere to play football.
"And we are hopeful, because there are a lot of committed people in Portsmouth trying to get this right and end up with a fan-owned club that will operate the club in the long term interests of continuing football in the city and the Football League are right behind that."