Hamilton has won six of his seven F1 championships with Mercedes overseen by team principal Wolff.
They are expected to thrash out a new contract during the winter that will keep Hamilton driving for Mercedes into 2024 and beyond.
“Toto is one of my best friends,” Hamilton said.
“We’ve had tough, tough times, we’ve had tough negotiations, there’s been emotional bursts, a rollercoaster of emotions together over the years, but we’re like family.
“I want what’s best for him. He wants what is best for me.
“We always can jump on the phone and talk about whatever that is. Our values are aligned and our goals are aligned – in the brand, in helping this team grow and what it wants to achieve.”
Hamilton is facing the first season of his career without a single F1 race victory, and has seen Max Verstappen rack up two consecutive championships.
“The hill that we have to climb is huge,” Hamilton said about returning to the title battle in 2023.
“It is important to imagine it as the biggest, steepest, toughest mountain you can climb because if you think it’s going to be a normal hill, you underachieve.
“You’ve got to think it’s the hardest climb you can imagine, which means you have to dig deep.
“There is a lot of work that we have already done up to this point to understand where we are, where we went wrong in the previous decisions that were made last year into this year.
“In terms of making the right steps for next year, it’s not easy to navigate as there are lots of different options but communication is what I’m trying to work on with everyone, making sure there are no loose ends, there’s no misunderstanding over what I feel in the car and what I want in the car, and making sure that we are continuously creating dialogue.”
He explained talking to trackside chief Andrew Shovlin, sporting director Ron Meadows and technical director Mike Elliott: “Just firing questions – ‘this is my concern, this is what keeps me up and night, what can we do about this? How can I help you do better, do more?’
“There’s not too much that you can do as we have to trust in the process, but it’s letting people know you are there – it’s not for them to figure out on their own, we will figure it out together.”
Hamilton is fifth in the F1 standings ahead of the F1 Sao Paulo Grand Prix.