The Briton won the season-ending Abu Dhabi Grand Prix on Sunday to come out on top in his gripping duel with Nico Rosberg, who missed out on a first world title after finishing 67 points adrift of his team-mate.
Hamilton has one year left on his contract with Mercedes and has been linked with a return to McLaren, but the 29-year-old envisages staying put.
Mercedes executive director Toto Wolff stated that the team are eager to tie Hamilton, who also won the title in 2008, down to a new deal and the Stevenage-born driver expects an agreement to be reached in the near future.
When asked if he sees himself at Mercedes for the next two to three years, Hamilton told Sky Sports News: "Without a doubt, and I hope longer. I've been a part of Mercedes since I was 13, so it's a natural progresion.
"During the season is not the time to really talk about things, and you start assessing and discussing the future generally in the last year of your contract.
"But we're happy with where we are and what we've achieved together. Toto was just saying in the coming weeks we'll sit down and hopefully it will be a simple process to go through - a formality."
Wolff said on Sunday: "We would love Lewis to stay in the team. He has been an incredible part in the development and rise of the team and we want to continue with both of them [Hamilton and Rosberg].
"I think he wants that too, but it is not a matter of a couple of hours of sitting down and just ticking the boxes. It needs proper reflection and discussion."