Lewis Hamilton wants to stay with Mercedes beyond his current contract, which expires at the end of 2015.
"We've both shown interest in sitting down and talking," said the Briton.
"The team know I would like to push to continue and they've made it clear they would like to do the same."
Hamilton joined Mercedes from McLaren, who also use the company's engines, on a three-year contract in 2013 and said he felt a strong bond with the company.
"I've been with Mercedes since I was 13," he said. "I very much feel like I have Mercedes imprinted on my chest. It's very much a family for me."
He added that he "can't see myself anywhere else".
|Hamilton's F1 record||McLaren||Mercedes|
|Years at the team||6||2|
Earlier this year Mercedes extended the contract of Hamilton's team-mate Nico Rosberg at least until the end of 2016.
Hamilton's contract expires at the same time as Red Bull's Sebastian Vettel, although the German is believed to have an option in his deal to stay for 2016 as well.
Asked about reports in the German media that Mercedes were interested in signing the four-time world champion, Hamilton said: "If they happen to want someone else that's the way it is. I'm not going to whinge about it. There are places for everyone."
He added: "I'm not worried about it. But another German driver? I'm not sure if it's something Mercedes would like.
"But at the moment I'm here until the end of next year so it's not going to be any time soon. But it's normal. Mercedes is the best and so everyone is going to want to drive a Mercedes."
Hamilton heads into the Hungarian Grand Prix this weekend determined to reduce Rosberg's 14-point lead in the championship.
He has won at the Hungaroring four times in the last seven years, and if he does so this year would break Michael Schumacher's record of wins at the track.
"I don't come here with an ambition to beat Michael's record," Hamilton said.
"I feel very privileged to have grown up and seen his success and now to be here and to be an F1 driver, but also to have had the same amount of wins here as he has.
"It's one of the coolest things to be able to put my name in the same sentence as his.
"I don't really have an answer as to why things have gone so well here. It's a great circuit. I enjoy driving it. Maybe it suits my driving style more than others."
Rosberg has never qualified or finished the race in the top three in Hungary but said he believed he could beat Hamilton.
"I'm very confident if I do a good job I'll be first and win the race," he said.
Red Bull are expected to be Mercedes' closest challengers around the twisty track, where the performance deficit of the world champions' Renault engine makes less of a difference.
Vettel said: "I always think there is a chance to win. It would be quite sad not to.
"Obviously Mercedes are very strong. Their drivers could probably go to the water park just outside the track on Saturday and still win the race.
"But they are not invincible, we have seen them have problems and then you need to put yourself in the best position to benefit so there is always a chance."