The National Theatre had hoped to transfer Robert Fox's production of David Hare's play Skylight, about an affair between a restaurateur and a radical young teacher, to New York with Gambon in the lead role.
But, following talks, American Equity has refused to let Gambon perform, arguing that the actor who played the lead in Dennis Potter's The Singing Detective is of insufficient "star status".
Its prohibition was confirmed by a spokeswoman at the National Theatre, where Gambon played the part of Tom Sergeant when Skylight opened last year. American Equity, the American actors' union, to comment on the decision described by Mr Fox as "eccentric".
Complicated rules presided over by the actors' union mean it can be extremely difficult for British actors to play in America if, like Gambon, they are not passed under the star status rule.
Producers are then obliged to prove that there is no American actor who can replace him or her in the part in question by carrying out auditions throughout the country.
The only alternative is for an actor to go to America under the exchange scheme, which allows an American actor of similar status to play in Britain in a straight swap.
Those who have previously fallen foul of Equity's perception of their star status (or otherwise) in America include Juliet Stevenson, who could not take her lead role in Death and the Maiden to New York, and Billie Whitelaw - despite her unique position as Beckett's muse.
Michael Pennington was also not deemed a big enough star, and missed the chance to act in Shaffer's Gift of the Gorgon on Broadway. Meanwhile, those who have been allowed include Elaine Paige, Tom Courtenay, and Vanessa Redgrave.
Such decisions raise the controversial question of what exactly is a star. Equity in Britain, which applies the same rule in reverse to American actors, admits it has never written a definition.
"It's impossible to say," admits Peter Finch, who heads Equity's theatre department. "It's often obvious, but if there's an element of doubt we would apply criteria such as what work that person has done, whether they have played in more than one country: and if so, which countries, and which theatre companies."
Jeff Kaye, European bureau chief of the entertainment industry paper the Hollywood Reporter, notes that British actors and actresses have been inhibited by traditionally being stereotyped into certain roles: the upper- class twit (a la Hugh Grant), the suave gentleman (Sean Connery's James Bond) or the evil villain (Alan Rickman).
"Michael Gambon rated 22 out of 100 in our star power list of the most bankable actors and actresses for last year," he added. "That's pretty low. Other Brits did far better. Kenneth Branagh was at 74, Sean Connery was at 94, and Hugh Grant was 81."
Stardom also differs in the worlds of theatre and film. Hollywood is about looks; the stage puts ability further up the pecking order.
"Theatre is much more about the quality of the actor because that's part of the experience of going to the theatre," said Nick James, deputy editor of the film magazine Sight and Sound. "In cinema it's to do with glamour rather than talent.
"Gambon rose to prominence in the English theatre as a marvellous stage performer, and that's enough on the English stage. But in the States he gets seen in movies where he plays parts more to do with hack-work - like Julia Roberts' father in the film Mary Reilly."
The problem is that any definition of what makes a star cannot include the imponderable quality which lifts a lead actor into a household name. That is an elusive mix of track record, personality, marketing, looks, enviability quotient, bankability and love life.
Emma Thompson, for example, seems to lack the enviability quotient, partly a result of her jolly-hockey-sticks looks. Daniel Day-Lewis, however, has a broodingly tragic appearance which fits the bill. The jury is still out on Kate Winslet: her looks and films so far are a plus, but her youth and naivete may prove a problem.
Of course, early death always helps in the quest for entertainment's holy grail. The ultimate star remains Marilyn Monroe, who combined a mysterious demise with an affair with the President, breathtaking looks and a tragic childhood.
Vanessa Redgrave in Orpheus Descending was accepted in the US because both Equities (UK and US) accept such "star'' performers without demur.
American Equity denied Billie Whitelaw star status, even though she was acting in plays Samuel Beckett wrote for her.
Sir Peter Hall's revival of Ibsen's Master Builder recently met the same fate. Alan Bates, who played Solness, was acceptable to Equity but Victoria Hamilton, who played Hilde, was a brilliant newcomer and thus taboo.