Hamilton is out of contract at the end of the year and speculation about his future is already rife as Mercedes struggle to recapture their past dominance.
However, Hamilton said he felt "amazing" about his future with the outfit.
"I continue to feel very much at home in this family," the Briton told reporters at Albert Park.
"I see myself with Mercedes until my last days, to be honest.
"I have amazing allies within the team, great relationships here.
"Just as long as I can continue to help drive the team forward, really contribute. If there's ever going to be a point where I feel like I'm unable to do that, it's time for a youngster to come in."
Having won six championships through a golden run with Mercedes, Hamilton failed to win a race last year, his first season without one.
Neither he nor teammate George Russell managed a podium in this year's season-opening races in Bahrain and Saudi Arabia, with Aston Martin's Fernando Alonso placing third behind both Red Bull drivers at each.
Mercedes have admitted they got their car concept wrong and have gone back to the drawing board.
Hamilton described the current package as a "little bit better" than last year's car, which was prone to bouncing, but said it could take the whole season to extract the performance from it to catch Red Bull.
"I'm aware that it can take a long time to catch the car ahead. You look at the Red Bulls, it's just going to continue to evolve," he said.
