And the expected venue for the transfer is the soon-to-be vacated Noel Coward Theatre, where The Full Monty recently posted closing notices - somewhat controversially - for 29 March (the same day, coincidentally, that From Here to Eternity and Stephen Ward also bow out).
Having originally premiered on Broadway, Good People won the New York Drama Critics' Circle Award for Best Play of the Year.
Staunton plays sharp-tongued single-mother Margie, who will do anything it takes to pay the bills after losing yet another job. Hearing that an old boyfriend who has made good is in town, she decides to corner him – old loyalties should be good for something.
The UK premiere production, which is directed by Jonathan Kent (who directed Staunton in Sweeney Todd) runs at Hampstead until 5 April.
Also in the cast are Lloyd Owen, recently seen in the West End in The Bodyguard, alongside Lorraine Ashbourne, Matthew Barker, Angel Coulby and June Watson.
If the rumour proves true, the transfer would precede the opening of Shakespeare in Love, which premieres at the Noel Coward in July.