"It needs an actor who can sing, dance, juggle, be a clown and an acrobat - and this man can do all of that," Mackintosh told the Daily Mail's Baz Bamigboye.
Fitzgerald's Broadway credits include Young Frankenstein, Finian's Rainbow and Wicked.
Barnum is reportedly being staged in a temporary 1400-seat theatre tent while Chichester's main venue undergoes a £22million development.
The role was originated on Broadway by Jim Dale, while Michael Crawford starred in the 1981 West End premiere at the London Palladium. The musical, which centres on 19th century American showman PT Barnum, has music by Cy Coleman, lyrics by Michael Stewart and a book by Mark Bramble.