Parry is back at his Anfield desk after being the guest of tycoon Robert Kraft and the Kraft family - owners of the MLS team New England Revolution and NFL team New England Patriots - at a match on Monday.
There are claims he was there to discuss major investment in the European champions to salvage their new stadium plans.
Parry has declined to admit such speculation but PA Sport understands at a board meeting last Thursday the Kraft family was only part of a discussion involving future investment in the club.
There is also believed to be a `rich middle eastern family interest' in Liverpool.
And it is already being suggested Parry's trip to Dubai for the Soccerex football business convention starting on Sunday for three days could also involve detailed discussions with future Liverpool backers.
Parry has issued a statement through the club's website www.liverpoolfc.tv regarding his visit to Boston saying: 'It certainly wasn't a secret visit having attended two games with a combined attendance of over 100000 people while I was there.
'I've actually known the Kraft family since meeting them in Boston back in 2001 and have had a long-standing invitation to visit the Gillette stadium which is one of the very few privately-funded stadia in the USA.
'They were keen for me to see at close hand how the match day operation ran and I watched both the New England Revolution v Chicago Fire MLS game on Sunday and the New England Patriots v Indianapolis Colts NFL fixture a day later.
'It also gave us the opportunity to discuss at length the way in which they had funded the construction of the ground.'
With the proposed new Stanley Park stadium estimated to cost £150million - initially it was just £80million - it is now accepted at boardroom level the scheme cannot be funded without outside investment.
The suggestions are Parry was in Boston to discuss the prospect of the Kraft family buying the naming rights to the new stadium in a similar fashion to Arsenal's new ground being named the Emirates stadium at a cost of £100million.
The Kraft family who have also been linked with the club before could also be prepared to buy a stake in the club.
Liverpool have been desperately searching for investors for almost two years and the Krafts were linked with a supposed bid from the US-based L4 Group last March which never materialised.
Liverpool have also previously distanced themselves from a £60million offer from Thai Prime Minister Thaksin Shinawatra for a 30% stake. Parry made a trip to Bangkok during those talks.
There have also been three separate share option bids from the club's third largest shareholder Steve Morgan and one was agreed in principle last season until the building tycoon backed away after a period of due diligence when he was able to view the club's books.
The spiralling cost of the new stadium was believed to be the reason for that failure with Morgan wanting to re-negotiate his bid to chairman David Moores.
Moores' desire to remain as a significant shareholder - he currently has 51% of the club - has always been the stumbling block for new investors.
At the top value of £4000 per share and with 35000 shares issued the club is valued at £140million. Moores has 18000.
Shares recently have changed hands at around £3200 each which would value the club at around £110million.
Liverpool do have 11000 extra unissued shares which could be sold to a new investor and that would reduce Moores' holding to 39% and see £44million of new money coming into the club.
But it is clear even if Moores sold his stake the cash involved would not go into the club coffers.
These are the problems that have been confronting Liverpool for some time and unless someone is prepared to buy out Moores fund the stadium and bankroll major transfer dealings there is no easy solution to the saga.