Britain's Alan Bates and Alan Rickman were also nominated in the category.
Schindler’s List star Neeson has wowed the critics with his role as persecuted John Proctor in The Crucible, while Gosford Park actor Bates has won rave reviews for his performance in Russian classic Fortune’s Fool.
Rickman plays Elyot Chase in Noel Coward’s Private Lives, which recently transferred from London’s West End. The production is also shortlisted for best revival of a play.
The trio line-up against Billy Crudup who plays the lead in British produced play The Elephant Man.
The National Theatre’s Trevor Nunn is nominated for best director of a musical for Oklahoma!, which is also in the running for six other wards including best choreography and best revival of a musical.
Howard Davies wins a nomination for best direction of a play for Private Lives.
Hit show Mamma Mia!, which was first performed in London, is up for best musical.
The Tony Award winners will be announced in New York on June 2.