The comic, whose parents came here from Iran, where his father was a reporter and his mother a dressmaker, is well aware of the rich ironies involved. He says that while the casting of an actor of Iranian descent as Fagin is in no way a political statement, it has nevertheless caused some comment in the Middle East.
Djaili, who is Baha'i rather than Muslim, explains that "I'm doing a show in Dubai soon and one of the papers there sent me a Q & A. One of the questions was, 'Isn't Fagin a strange role for you to be playing? Which meant: 'what on earth are you doing playing a Jew?' So there have been some raised eyebrows."
The comic, whose stand-up act includes a masterful piece of cod belly dancing, adds that, "my own eyebrows were raised, too. Fagin is one of those roles that I never, ever thought I'd be considered for. I never thought Rowan Atkinson would bow out. It's his show – why would he stop?
"Even my agent didn't think of me for the role. Oliver!'s casting director asked my agent, 'Can you think of anyone for Fagin?', and my agent said, 'No!' Then the casting director said, 'Don't you represent that Iranian guy who makes people laugh by belly dancing? Can we see him?'" In the end, the offer was impossible to turn down. There is also no doubt Djalili will have the requisite presence for the role; in his comedy act, he erupts on stage in a star-burst of captivating energy.
"Playing Fagin is such a delicious extra string to my bow that I couldn't resist it," the comedian beams. "It's a very creative piece of casting. If I wasn't me, I'd say, 'wow, I'd go and see that show out of curiosity!'"
Djalili, who describes himself as "Iran's answer to Carol Vorderman", approached the audition for Fagin in typically unorthodox fashion. "I did 'Reviewing the Situation' and threw in a few Middle Eastern phrases, which made them laugh."
The performer reveals that he will be portraying Fagin as "playful. Rowan's first line is a very Blackadder-ish 'what?', which gets a huge round of applause. I might come on and break into Jackie Mason!" Segueing into an immaculate Mason impersonation, Djalili continues, "Bill Clinton says oral sex is not sex. Now all the guys in Miami are calling their hookers to try to get their money back."
The performer is an accomplished actor whose impressive film CV includes Gladiator, Pirates of the Caribbean, The World Is Not Enough and Casanova. However, he will admit to some nerves about making his musical debut in such a high-profile show and succeeding such illustrious performers in the role.
"It's not only Rowan. I'm also following in the footsteps of people like Robert Lindsay and Jonathan Pryce. To be compared to those top actors is frightening. But it's still an absolute thrill to be involved in this production.
"They've spent millions on it, and there are 2,500 people in the audience every night. I'm excited about that. I won't be shaking and dry in the mouth. Doing live comedy, I've learnt to savour these big shows."
Married with three children, the 43-year-old is an engaging, eclectic character, able to discuss suicide bombing and showbiz with equal facility. The first series of The Omid Djalili Show attracted a lot of comment, as the comic courageously tackled topics which were previously considered off limits to comedians, such as Islamic fundamentalism and terrorism.
"I suppose it is brave to address these subjects in the context of what else is in mainstream comedies," reflects the performer, who read English and theatre studies at the University of Ulster. "You certainly don't get that in I'm a Celebrity ... Get Me Out of Here!
"But I believe no subject is taboo if it's done in the right way and with sensitivity. If the audience trust you, I think you can about anything, you really can. If you're clear about your motives, then you can cover any subject with a clear conscience. Of course, some people will be offended, but if you can justify your humour, I think it's fine."
Rather than preaching to his audience, Djalili believes it is far more effective to smuggle in more serious points via the Trojan Horse of comedy. For instance, in his TV show he highlights the horrendous effects of the recession on on ordinary families through the ludicrous form of "Credit Crunch – the Rock Opera".
He also suggests that the government borrows £180bn from the only people in the world who now have sufficient liquidity: Somalian pirates. He goes on to perform the best (and only) impression of a Somalian pirate I have ever heard.
"I try to avoid being didactic," reflects Djalili. "You can't wave a political banner in comedy. There's this great line from Brendan Gill: 'not a shred of evidence exists in favour of the idea that life is serious'. In comedy, if you're trying to make serious points, you can't make them in a serious way. I like silly. And what could be more silly than a bunch of forty-something blokes dressed as mini-cab drivers doing a song and dance routine?"
Djalili is viewed as a standard-bearer for the British-Iranian community, but the tag does not sit comfortably on his shoulders. "I don't want to be a role model," he asserts. "I'm just comedian. If British-Iranian companies are keen for me to be a standard-bearer, they should show that in their corporate fees!"
He says 98 per cent of the British-Iranian community are proud of his success, but two per cent of them still cavil and ask: "why does our best-known Iranian have to be bald and fat? Why can't we have someone better-looking as a role model?"
So what does the comic hope that viewers will take away from the current series of The Omid Djalili Show? Donning a mock-earnest expression, he deadpans "just put: 'Djalili wants to bring about world peace by means of stand-up. He feels he achieved that in the first series, and so for the second it's off to the moon'."
He goes on to tell me what he is doing next. He is starring in an intriguing-sounding movie written by his fellow comedian David Baddiel.
In The Infidel, Djalili portrays an adopted Muslim who discovers that he is in fact the son of a Hassidic Jew. "This year I'm playing Fagin and the world's first Muslim Jew. If I'm not embraced by the Jewish community now, I never will be," he laughs. "I've done everything I can!"
The Omid Djalili Show is on BBC1 on Mondays. He joins the cast of Oliver! as Fagin for six months from 20 July at the Theatre Royal Drury Lane, London
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