But Lord Lloyd-Webber hopes that domestic talent will be plentiful enough for Bombay Dreams' casting, when youngsters start attending auditions in January.
The very best of the young talent will then be offered training and a contract to appear in the show.
Lord Lloyd-Webber said: "When we first started the project we carried out national auditions to find a cast that we felt would do justice to the story, music and lyrics.
"We have done that and now we feel it is time to offer this amazing opportunity to others too."
A spokesman for the actors' union Equity said he was not aware of how many of its members were British-Asian.
But he said: "We are not opposed to open auditions and want to encourage new and talented people to enter the entertainment profession - we are very much in favour of this kind of training."
He added: "Of course, if it is an open audition, I'm sure existing professionals who think they fit the bill will try as well."
Jaffrey, who plays Akaash in the show, hopes the auditions will inspire stars of the future to come forward.
He said: "Bombay Dreams is unique in giving Asian talent a chance to shine - and I hope that more and more people see theatre, drama and acting as a real career opportunity now that a precedent has been set."
Anyone who wants to audition for a part in Bombay Dreams must be over 16 and should submit a CV and photographs to David Grindrod Associates, Bombay Dreams, The Palace Theatre, London, W1V 8AY.