Although both sides have indicated that they intend to sign a new contract beyond 2018, until now a deal has been delayed as "details" are negotiated.
However, when asked what the future holds for him, quadruple world champion Hamilton answered: "My hope for the future is that we continue.
"I really want to take this team the furthest it has ever been.
"I want to be part of this journey where Mercedes are the most successful Formula 1 team in history."
Hamilton often gives mixed messages about how long he will remain committed to F1, but he now indicates that he wants a long-term deal to stay at Mercedes.
"I want to push it as far as I can, with the lifespan as a driver that I have, that it would take a long, long time for anyone else to catch up," he said.
"I think it would really upset the red cars and the red team, so that's my goal."
Hamilton is second to Sebastian Vettel in the drivers' standings ahead of this weekend's Azerbaijan Grand Prix.