One of the stipulations of the test is that an owner or director cannot have been involved with a club that has twice gone into administration.
Chainrai was in control of Pompey when they
went into administration in 2010,
and may have had some involvement as a shadow director when they were placed into administration for a second time in February 2012.
Portpin has always denied this is the case.
"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," added the statement, issued to BBC Sport's Matt Slater.
"We are very confident that we are in a position to complete the acquisition of Portsmouth Football club in the near future."
The Hong Kong businessman is owed £17m by the club and holds Fratton Park as security.
The League has refused to comment publicly on Thursday's meeting but did confirm to BBC Sport on Saturday "the board were given an update on the current situation".
Although this is good news for the Trust, there is still a long way to go before any deal is finalised.
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