The celebrity couple are planning to head over to Los Angeles next year following their respective appearances in stage shows.
Fox said that he has "no preconceptions" over their plans, but they are looking to try living in America for a while in order to attempt to find acting work in Hollywood.
"We could go there and not get a job and they could say, 'You suck', and we come home. Who knows what's going to actually happen?" he told the Evening Standard.
Fox is currently starring in West End play Our Boys, while Piper stars in The Effect at the National Theatre until January 2013.
Piper and Lewis actor Fox welcomed their second child Eugene Pip back in April.
They are also parents to 3-year-old Winston, having married in 2007.