"Why not?," he told Wednesday's Guardian newspaper, after the Briton's third podium finish in three races at the weekend. "It's obviously too early to analyse but if the trend continues there is no reason why he could not be the greatest driver ever."
Whitmarsh, who has worked at McLaren with the likes of Brazilian Ayrton Senna and France's quadruple champion Alain Prost, said he had "a pretty clear picture of what gives the top guys that crucial edge over the simply good or average drivers.
"And I think it is pretty clear that Lewis ticks all the necessary boxes."
Hamilton, 22, came second and beat his double world champion team mate Fernando Alonso in Sunday's Bahrain Grand Prix after finishing runner-up to the Spaniard the previous weekend in Malaysia. He had been third in the Australian season-opener.
His phenomenal start to the season, admittedly in one of the best cars on the starting grid, made him the first Formula One driver in the 57-year history of the world championship to finish his first three races on the podium.
It also left him, with Alonso and Ferrari's Kimi Raikkonen, in a three-way tie at the top of the championship with 22 points.
SURPASSING EXPECTATIONS
Formula One greats Jackie Stewart and Stirling Moss acclaimed the youngster's performance and attitude after Melbourne and the accolades have continued to flow in as Hamilton surpasses all expectations.
"Within the next three years, Lewis Hamilton will certainly be in contention and could easily win the world championship," Stewart told the Sun newspaper.
"It's not inconceivable it could be done this year...he's been able to accomplish more in a shorter time than any driver I've ever seen."
Team boss Frank Williams, whose cars took Hamilton's compatriots Damon Hill and Nigel Mansell to the world title, joined the chorus of admiration after the weekend.
"I thought after we got rid of Michael (Schumacher), now we've got a chance again," he said. "But then another superhuman turns up.
"Michael was many things, but he was also a very, very simple human. Hamilton is a different character I think, but purely in terms of calibre or quality of skill, what I'm seeing so early in this man's career is remarkable."
Hamilton entered Formula One after winning last year's GP2 title and has been nurtured carefully by McLaren for the past decade.
He has made no mistakes so far, although team bosses admit errors are inevitable in one so young and inexperienced.
"I think he's at the point where he's got enough brownie points in his pocket to afford to lose some without getting heavy criticism," team boss Ron Dennis told reporters in Bahrain at the weekend.
"We've tried to keep the pedestal low, because inevitably he will fall, or step off it," he continued. "That's the time, because inevitably they all make mistakes, when he will get some criticism.
"But for the moment he can't do anything wrong, can he?"
