Hamilton returned for the Abu Dhabi Grand Prix last weekend and finished third behind Bottas and winner Max Verstappen.
He has said it would be nice to have a new contract in place for Mercedes next season before Christmas.
He explained: “I plan to be here next year, and I ought to be here next year.
“As a team, we have more to do together – more to achieve both in and outside of the sport.
“I hope we can begin discussions this week and then hopefully get it tied up before Christmas.”