The 52-year-old Briton, who took over at the helm from Ron Dennis last season, told reporters at the German Grand Prix [ Images ] that what might once have been a fantasy could become a reality in his lifetime.
McLaren, he suggested, were riding a wave of support driven by British drivers Lewis Hamilton [ Images ] and Jenson Button [ Images ], the last two world champions who are first and second in the standings.
"The biggest brand in Formula One today is Ferrari, and I acknowledge and accept it," he told reporters in the McLaren 'Brand Centre', an imposing glass-fronted structure in the Hockenheim paddock.
"McLaren I think is the second biggest brand in Formula One by a reasonable margin from whoever is the third.
"They (Ferrari) have got 60 years of heritage, lots of world championships. Rather than me be jealous of it or pretend its not there, it's much better to say they are fantastic, they have achieved so much, but we want to beat them one day," he continued.
"It might not be even in my career but in 10 years, 20 years time why can't we be the biggest brand?
"Twenty years ago that would have sounded ridiculous to say, I don't think it sounds so ridiculous now and hopefully in 10 years time it will sound even more realistic and in 20 years time we'll have done it."
Whitmarsh said he had noticed a change at this month's British Grand Prix when he drove in to the circuit and had to wait for a stream of supporters to cross the road.
More than half were wearing McLaren branding while there was barely a Ferrari cap or shirt in sight.
That undeniably had much to do with Hamilton and Button competing at their home grand prix.
The two Spanish races, home of Ferrari's Fernando Alonso [ Images ], had far more of the Italian team's branding on show, as will the season-ender in Abu Dhabi with a Ferrari theme park next door.
However, Whitmarsh said his team, who had champions like Ayrton Senna and James Hunt, were now more popular than ever.
"I have never experienced in whatever, 22 years in this team, the feeling of support that we are enjoying," he said.
"I have to say it's largely down to the drivers. One, their performance in a car but also their performance out of a car. They are both attractive personalities, honest human beings that I think people can relate to and there is a tremendous feeling.
"We've had times when we've been performing well, winning races, easily winning championships but we have never felt the support that we've had this year," said Whitmarsh.
McLaren and Ferrari were once sworn enemies, their rivalry triggering bitter controversies, but that has softened since the departure of Dennis and former Ferrari boss Jean Todt.
They are now united in the Formula One Teams Association (FOTA) led by Whitmarsh and on a far more friendly footing.
"We talk much more affectionately about Ferrari now than we ever have, and I do have a lot of respect for Ferrari as a brand and as a race team and the people that run it," said Whitmarsh.
"But nonetheless for years you saw Ferrari merchandise ... everywhere around the world in Formula One venues, and you've got to say there's considerably less now.
"Go back 20 or 25 years and there was the Ferrari brand and the rest of us. I think McLaren has pulled itself up and therefore we are sharing some of that with Ferrari in a way that we weren't before."