Administrator PKF nominated The Portsmouth Supporters Trust (PST) as preferred bidder for the former Premier League club last month, choosing the fans' group over Chainrai's Portpin company.
Portsmouth, FA Cup winners in 2008, went into administration in February and their debts are reported to be around £61 million pounds. They were relegated to League One at the end of last season.
Portpin said progress on completing a deal "appears to have been non-existent" since the Trust was named as preferred bidder on October 18.
"Therefore, until the PST bid has been validated and reviewed by the Football League, it seems that there is little point in Portpin pursuing their bid further," the company said in a statement.
Hong Kong businessman Chainrai said he believed frustration over the delay was why Michael Appleton left this week to take the manager's job at second division Blackpool.
Portpin are still owed £17m by the club, secured against its Fratton Park stadium. That would mean the Trust would need to agree a deal to buy the ground were their takeover to go through.
Portpin accused PKF of charging "exorbitant fees" of more than £3m since Portsmouth went into administration nine months ago.
There was no immediate comment from PKF.