National hero: Pienaar will be played by Matt Damon in Invictus

A movie directed by Clint Eastwood, telling the story of South Africa's 1995 World Cup triumph and Nelson Mandela's hope that it might unite a nation, has its premiere in the United States next month. In it, a muscled-up Matt Damon plays the role of Francois Pienaar, the Springbok captain. The star of the Bourne trilogy can be relied upon to get the acting right but at 5ft 10in to Pienaar's 6ft 3in he has one obvious shortcoming.

"My wife was delighted that Matt was playing me," says Pienaar, with a chuckle clearly audible down the phone line from Cape Town. "But she was not impressed when I invited him to my house and said I'd do the cooking. Matt's first words when I opened the door were…well, he looked at me, he didn't even say 'hi', he just said 'I'm much bigger in the movie' and then he hugged me."

Damon, as Pienaar quickly concluded, belonged in a category distinct from mere sportsmen, even world-renowned ones forever bracketed after 1995 and all that with a totemic statesman like Mandela. "One night I was having a glass of vino with Matt when I told him about our Make A Difference charity's 110km cycle ride around the Cape to help disadvantaged children and he said he'd do it with us. This was rock-star stuff. Everywhere there were people with banners and good-looking ladies shouting 'Matt! Matt'!"

Pienaar has yet to see the film, in which Morgan Freeman portrays Mandela, but he visited the set with his two sons, and he and John Carlin, whose book Playing the Enemy was adapted for the screenplay, consulted with the leading lights. "Obviously it's Hollywood and to dramatise the movie and for it to reach a crescendo there's a lot of licence in the screenplay," says Pienaar. "I'm very excited to see it in December, but there's also that little sense in me that's saying, 'I just hope they catch the moment like I remember it'.

"Did Nelson Mandela really ask me to win the World Cup? That's where the licence comes in. I met Madiba [Mandela's honorary name in his clan] in '94 and he never spoke about the World Cup. We spoke about our tour to New Zealand, and about the Olympic Games and about boxing, and about his village where he had to adjudicate an affair where somebody stole a lady's chicken.

"In the end, though, it's a magnificent story and I was privileged to be involved in that story. Morgan Freeman went into Mandela mode a couple of weeks before shooting – talking like Madiba, with his mannerisms. It was scary and, wow, it was impressive. Morne du Plessis [the Boks' manager in 1995] told me when he saw the prosthetic being applied to Matt's nose to look like mine, 'Oh my goodness, this is too close to the truth'."

Invictus comes to the UK in early February, but the trailer is out now, with Freeman's husky take on Mandela's measured tones: "I am the master of my fate, I am the captain of my soul." Pienaar captained Transvaal and South Africa before heading north to Saracens in 1996 as player and eventually skipper, coach and chief executive. The hitherto humdrum north London club did not win much under their eminent import – one domestic cup in six years before he headed home – but Pienaar never lost touch with the club's chairman, Nigel Wray.

Last year Pienaar put the billionaire investor Johan Rupert together with Wray, and a 50 per cent South African shareholding in the club followed. With Pienaar and Du Plessis appointed to the board, and 13 South African-born players and coaches added to the squad, Saracens are currently top of the Premiership. On Tuesday they will host the Springboks – world champions once more following their win in 2007 – at Wembley. The on-field MC, after he has flown in for tomorrow's quarterly board meeting, will be Pienaar.

"I saw the opening match this season at Twickenham and the Wembley game against Northampton," he says. "Brendan Venter as coach has worked hard on getting the team to play for one another. They fight for every blade of grass, and they are winning close encounters – it's almost as if they refuse to lose." Hiring Wembley runs well into six figures for each match, and Sarries can also afford stunts like Tuesday's £250,000 prize if one of three fans can hit the bar with a punt from 30 metres.

If world domination is on Rupert's wish list, surely he has the bank balance to make it happen? "It's a work in progress," Pienaar says, with caution. "They're trying all angles to broaden the base of season ticket-holders to 13,000 or 14,000 to make it financially viable.

"The focus in the next couple of years is being competitive in the top four of the Premiership. Getting into the Heineken Cup is very important."

But when it comes to the South African influence, Pienaar, who runs a sports marketing business, is more bullish. "Look at London Irish, they hardly have an Irish player. Look at Arsenal and how many foreign players they've got. It doesn't affect the passion around the club. It's about the brand and how that brand is portrayed and whether it's successful."

Pienaar, now 42, is enthusiastic about his Springbok successors and about rugby in general. "I think the game is really in a sweet spot. The hits going in these days are big, they're wonderful to watch. That's the game. It's a collision sport."