Candidates for the British stage’s most influential role are jostling for position after it emerged that Sir Kenneth Branagh has been approached to become the next artistic director of the National Theatre.

Should he accept, Branagh, 52, would emulate his hero, Sir Laurence Olivier, who successfully combined British theatre’s most prestigious post with an active screen career, when he became the NT’s first artistic director in 1963.

But Branagh’s is not the only name in the frame with informed sources suggesting that Rufus Norris, who recently directed The Amen Corner at the National, is being considered.

The NT is currently considering a successor to Sir Nicholas Hytner, who has presided over a hugely-successful decade marked by hit shows including One Man, Two Guvnors, who announced that he is to step down at the end of March 2015.

Belfast-born Sir Kenneth’s interest in the South Bank position was revealed by Sir Anthony Hopkins, who received a personal email from the actor-director.

The Silence of the Lambs star said: “He wrote me an email and told me he’d been offered the directorship. I said do it, because he’s the only actor who could replace Olivier today. I told him he must accept. You see, Ken has got the teeth and the guts to do it.”

The National job would offer a fitting pinnacle to his illustrious 30-year film and stage career, having followed in Olivier’s footsteps by adapting, directing, and starring in big screen adaptations of Henry V and Hamlet.

In 2011, Branagh said: “I have a pathetic urge at some stage in my life to be able to pull out my wallet and pull out a little card on which it would say Kenneth Branagh, artistic director.” However, there have also been suggestions that he was being lined up to take over from Kevin Spacey when the American star stands aside as artistic director of London’s Old Vic theatre in 2015.

A spokesman for Sir Kenneth, who played Olivier in the Marilyn Monroe biopic My Week With Marilyn, said that while he had not applied for the NT job, he had discussed an approach with Sir Anthony who is a “dear friend and valued adviser”.

Informal approaches are also believed to have been made to the ex-Donmar Warehouse bosses Sam Mendes and Michael Grandage, and the theatre and film directors Stephen Daldry and Danny Boyle.

Mendes, who has signed up to direct the next James Bond film, set for an October 2015 release, said he was “interested” in the post but concluded that “if I run the National Theatre I can’t direct movies”. Grandage indictated that he would be “uneasy” with the public side of the role and wanted to stick with directing.

The NT board began conducting initial interviews during the summer. Rufus Norris, an associate director whose productions include Festen, which transferred to Broadway, is among those believed to have been interviewed. Other contenders include former Royal Court artistic directors Ian Rickson and Dominic Cooke and War Horse director Marianne Elliott, another associate director at the NT.

The board is said to have received proposals for a “joint directorship” from some of those who are reluctant to take on the post alone but the favoured option is believed to be a single individual.

The National Theatre did not deny that Sir Kenneth had been approached over the role. But a spokesman said that he “has neither applied for nor has been offered the job of Artistic Director at the National Theatre”.

Starring roles: NT artistic directors

Lord Olivier (1963-1973)

Reign marred by Board’s cancellation of 1967 play Soldiers, which alleged Churchill ordered death of Polish PM and suggestions he blocked roles for John Gielgud and Ralph Richardson through jealousy.

Sir Peter Hall (1973-1988)

Presided over 1976 move from the Old Vic to the South Bank. Highlights included Bedroom Farce, directed by Sir Peter.

Sir Richard Eyre (1988-1997)

Launched era-defining new plays including Tony Kushner’s Angels in America and the David Hare Trilogy.

Sir Trevor Nunn (1997-2003)

Oklahoma! and My Fair Lady kept the box office buzzing but stepped down after single term following failure of The Villain’s Opera and two troubled plays had to be dropped.

Sir Nicholas Hytner (2003-2015)

A golden spell with shows such as Jerry Springer: The Opera, War Horse and One Man, Two Guvnors, transferring to the West End.