The American duo want to modify existing plans to ensure a fresh planning application won't be required and any delay in building work takes weeks, not months or years.
Gillett and Hicks met planners when they visited Merseyside last week, when their ambition to extend the capacity from 61,000 to 76,000 - the same as at Manchester United - was underlined.
They're now working as quickly as possible to make the revision in a way that works for the city planners.
One possibility is proceeding with the plan to build a 61,000 capacity, but with a provision to extend at a later date.
More details on their proposals are anticipated when the duo return to Liverpool on March 31.
In the meantime, building of the new Anfield Stadium has been temporarily suspended.
"They are conducting a very swift review of what is possible," explained Reds chief executive Rick Parry.
"Yes work has been halted very temporarily, but their commitment to the new stadium is total. There's no question of that.
"But if there is going to be a review of what might be possible, now is the time.
"If there are going to be any changes, however, it will be a case of scaling up, not downscaling.
"They are experts in this field and I'm constantly hearing phrases like 'best in the world'.
"They just want to understand exactly what the options are for the future. If there are ways of constructing the stadium which would allow for future expansion, they want to investigate it.
"It makes perfect common sense.
"They don't want to steam ahead into something which might prevent expansion in the future.
"Construction deadlines won't change, however. Any changes will be discussed in the next few weeks and actual building-work will commence on the planned date."
Among ideas being considered by the Americans are "bunker suites" - executive boxes built underground, with lifts to and from the seats in the stand above.
The idea was developed by President George W Bush when he was joint owner of the Texas Rangers baseball team, which Hicks now owns, to offer a place for his father, who was President at the time, to watch games securely.
More are planned for the ground at Arlington and at the 100,000-capacity stadium being built nearby for the Dallas Cowboys, which is due to open in 2009.
Last month Hicks explained: "We met with HKS (US architects) and we said, 'Here are the constraints, take a fresh look and see if there are other ideas we can incorporate on the inside that would make it more fan-friendly, produce more revenues and give more customer satisfaction', they areworking on ideas.
"What we have to do is strike a balance between new ideas and Yankee ingenuity at the same time as protecting the traditions of Liverpool and Anfield. We're going to do that very quickly.
"We kind of stumbled into the concept of the bunker suites. But it's essentially an underground living room where you can go down and have fine food, fine wine, big-screen TVs, and then go up and watch the pitch live."
Hicks wants to replicate the way he has used sports stadia to regenerate run-down areas of Dallas.
He has done it with the American Airlines Centre, a £210 million arena which is home to the Dallas Stars and Mavericks. He also has plans to redevelop 1.2 million square feet of land next to the Arlington stadium into a leisure, retail and residential complex in a £260 million project, which will open in 2009.