The 25-year-old Briton entered the sport the year after seven-times champion Schumacher retired from Ferrari in 2006, and this weekend is the first time the two have raced each other around the streets of Monaco.
The German’s comeback with Mercedes, at the age of 41, has revived memories of his last appearance in Monaco when he was sent to the back of the starting grid for blocking the track in qualifying to secure pole.
That controversy was one of several to have dogged Schumacher’s career despite his status as the most successful driver the sport has ever seen, with 91 wins.
Hamilton, the 2008 world champion with McLaren, said he would hate to walk away from the sport with his reputation similarly “tainted”.
“When I leave F1 I want to be remembered as one of the best drivers of all time,” he told Reuters in the harbour-side paddock.
“I am not really bothered if I am remembered or not. But clearly I am going to be remembered. I am part of the sport, I’m part of its history, I am a world champion,” he added.
“I think as I am going to be anyway, I would like to be remembered in the best way and the best light,” added the driver, who was himself embroiled in a furore over lying to race stewards last season.
He said that was not just as a champion.
“I want to be remembered as a fair driver as a clean driver and one that always drove with my heart and battled through thick and thin to score the points and the championships I will hopefully earn by then,” explained the Briton.
“For me, when I think about the history it is not just about me, it is about how my family raised me, and where we came from.
“For that to be potentially tainted by something like that (Schumacher’s Monaco controversy) would be really devastating for me. That is definitely something I don’t want to be remembered for.”
Hamilton refused to be drawn into a judgment on what Schumacher did last time around, however.
“I just focus on my own job. It doesn’t have any impact on me. You guys have an opinion about it… whether I think it was right or wrong I wasn’t in the car with him,” he said.
The prospect of racing Schumacher, a five-times winner in Monaco, might once have been a big thrill but not any more for a youngster who has achieved so much already in three seasons in the sport.
“It doesn’t do anything for me whatsoever,” he said.
“He is a world champion and you want to be up against a world champion. It is always a privilege to be on the same track as him as it is having him in the sport.
“It would be special if I was on the track with (the late Brazilian champion) Ayrton (Senna), for me, but everyone has their own points of view.”
Schumacher lapped faster than Hamilton in both of Thursday’s practice sessions.