PKF have said they will work with the PST and resume talks with the Football League to bring the club out of administration.
Balram Chainrai had previously been PKF's preferred bidder but it is understood the Football League has raised concerns over his suitability.
"After extensive discussions over the past few weeks, we have today nominated Portsmouth Supporters' Trust as the preferred bidder for Portsmouth Football Club," confirmed joint administrator Trevor Birch.
"We will be working with the Trust, the Football League and the Professional Footballers' Association to conclude the sale of the club as soon as possible."
The PST has been vying for control of Pompey with former club chairman Chainrai's company Portpin for several months now.
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 but PKF has now turned to the PST as it looks to bring the club out of administration.
That scenario is still a long way off and the PST still has to satisfy the Football League of its suitability while it will also need to go through the 'owners and directors' test.
The PST is led by Ashley Brown and backed by, among others, local businessman Iain McInnes.
McInnes would become Pompey chairman if it was to take over the club and he hailed PKF's decision.
"We are energised that our bid, by the fans and for the fans, has been preferred by the club's administrators," said McInnes in a statement.
"Although there remains a huge amount of work to be done to ensure the right outcome for the club, we are confident we will succeed.
"We believe our bid is realistic and credible, which is a view shared by the administrator. We will be working closely with Trevor Birch and his team in the coming days and weeks to ensure our bid will meet all legal and financial requirements."
The Trust will also needs to satisfy the Football League it can sustain the ownership of the club in the long term.
Any takeover is also likely to be met with resistance from Chainrai, who is still owed around £18m by the club and holds Fratton Park as security.
The PST has offered Chainrai £2.75m for Fratton Park. If he refuses to sell the Trust could try to force a court to release his charge on Fratton Park and sell the stadium at the market rate.
Another possibility is that PKF could ask Portpin and the PST to reach an amicable solution for the sale of Fratton Park.
If not, that could lead to a costly legal fight that would ultimately put the club into more debt.
In a statement issued to BBC Sport, Portpin said it would continue to fight to take control of the club.
"We continue to work with the Football League to ensure we are ready to complete the acquisition of Portsmouth Football Club," it said.
"Our discussions remain productive and we have been given no reason to believe that there are any remaining obstacles to our bid.
"Whilst we note PKF's decision, we recognise that preferred bidder status has no basis in law.
"And we are confident that our bid offers both the best deal for creditors and is the only fully funded offer to provide Portsmouth FC with a financially sound and sustainable future."