Pompey have been in administration since February and the club will go bust if a takeover is not completed.
It is the second time the club has been in administration in two years and Chainrai was at the helm the first time in February 2010, before selling to Vladimir Antonov.
Portsmouth went back into administration this year during which time Portpin retained a charge over the club's assets and Fratton Park.
Chainrai is now looking to take over the club but reports on Saturday questioned whether he will pass the fit and proper person test as Football League rules do not allow a person to own a football club or be a director if he has previously twice been a director or owner of a club when it has fallen into administration.
Following those reports on Saturday, the Hong Kong-based businessman released a statement that said: "Our discussions with the Football League have been positive and are progressing.
"As far as we are aware we have satisfied the majority of the criteria and we expect now to work through the last remaining points with the Football League in the coming days.
"We are very confident that we are in a position to complete the acquisition of Portsmouth Football club in the near future."
The reports also suggested administrators PKF are set to resume discussions with the Pompey Supporters Trust (PST) next week over its takeover proposal.
The trust, which could be presented to the Football League as preferred bidder, is expecting to hear from administrator Trevor Birch soon and remains resolute in its attempts to buy Portsmouth.
"The PST position has always been clear that we have got what we believe is a credible bid," said PST spokesman Colin Farmery.
"It has been on the table since June and we've always said that we're ready, willing and able to buy the club.
"Obviously we've seen these interesting stories overnight that have come out in the media.
"As far as we're concerned, we're in an on-going dialogue with PKF and we're expecting to get further clarification next week.
"We wrote to the Football League about a fortnight ago outlining our concerns as to why we thought that Portpin should not actually pass their owners and directors test.
"The Football League met on Thursday and nothing official has come out of that meeting at the moment."