Hamilton, set to compete in Bahrain in the second round of his world championship defence on Sunday, remains F1’s first and only black driver.
The 34-year-old British star has spoken about the absence of diversity in the sport.
On Tuesday, he tweeted in support of the England footballers who were subjected to racial abuse in Montenegro.
David Richards, chairperson of Motorsport UK, believes the weight of Hamilton’s name in supporting its initiative aimed at increasing participation would prove a huge boost in changing the make-up of the sport.
“We are talking with Lewis and we have had discussions of that nature,” Richards told Britain’s Press Association.
“I am sure in future years that Lewis is going to be a great ambassador for us in helping to attract and appeal to disadvantaged children in inner cities, who may kick a football around, but the last thing they would ever dream of being able to do is drive a racing car.”
Richards, a former F1 team boss who will be in Bahrain this weekend, added: “It is early days, and Lewis’s priority is to win a couple more world championships, but I am quite certain that he will be looking for a legacy.
“I hope that will be by assisting us to expand the grassroots level and footprint of motorsport into areas where we haven’t been in the past.”
At last year’s Australian Grand Prix, Hamilton addressed the ethnic issues facing F1.
In an Instagram post he wrote: “There’s barely any diversity in F1. Nothing has changed in the 11 years I’ve been here.“
And on the eve of the new campaign, Hamilton again reiterated his interest in improving diversity. He said: “What’s driving me right now is to continue to push for diversity, to push for change.
“Not only in my sport but also in the world and encouraging people in general but naturally youngsters who are up and coming and have dreams.”
Hamilton trails Mercedes team-mate Valtteri Bottas in the standings following the Finn’s victory at the season-opening Australian Grand Prix earlier this month.