The European champions are no more likely to admit that their chief executive's trip to the Soccerex Convention, taking place in the "City of Gold" these next three days, is any more notable than his much-trailed sojourn last week to meet Robert Kraft, the owner of the New England Patriots. But sources high up in the Liverpool boardroom admit that there is more to Parry's movements than simple reconnaissance missions. Dollar-finding, yes. Fact-finding, if only.
The potential backers awaiting Parry at the annual "business of soccer" extravaganza have been described as "a rich Middle East family" - in football speak, is there any other kind? - whose interest in the Merseyside giants has been known for some time. After the calamity of the Thailand prime minister's attempts to buy a 30 per cent share last year, the Anfield hierarchy were understandably twitchy about whom they should and shouldn't be linked to, but matters are coming to such a head that necessity is outweighing PR. While David Moores is far from being a beggar, the Liverpool chairman is way past being a chooser.
The £120m of private funding the club need to proceed with the new stadium at Stanley Park dictates he can't be, as do the worrying whispers emanating from America saying that Kraft - a paper/packaging billionaire who is no relation to America's biggest food manufacturer - only has eyes for Moores' entire 51 per cent shareholding.
Moores is palpably against relinquishing it all and Kraft is reportedly not keen on either taking a smaller stake or buying a naming-rights package for the new stadium similar to the Arsenal-Emirates deal. As an owner who has basked in the glory of three Super Bowl victories since 1994, Kraft, unsurprisingly, wants his name above the door and not on the back of the main stand. Therein lies a problem that is in danger of becoming perennial for Liverpool. After the miracle of Istanbul, Moores seems determined to keep some measure of control over a club he has never felt closer to, and even if he was prepared to sell - as he was last season to Steve Morgan, a local building magnate - the club would be looking for a suitor with the wherewithal to buy out Moores, pay for the stadium and fund the transfer spree Rafa Benitez craves.
Otherwise, there is only the long-awaited, and hence ever-diminishing, prospect of outside investment to keep the Stanley Park development a reality without sacrificing Benitez's plans, as it was revealed last week that unless it can be proved by February that Liverpool have the required private funding to build a stadium which could yet cost more than £200m, up to £20m of European and local development agency money could be forsaken.
In the light of this and scepticism that Dubai will turn up gold for Parry, it is hard to disagree with the feeling that a redevelopment to bring Anfield up to 60,000 is the most likely eventuality. Still, walking alone has never been considered the easiest option at Liverpool.