Hamilton, like the Mercedes chief, is set to sign a new three-year contract.
The report claims he did hold talks with Ferrari about a potential move but, now, their loss is to be the Silver Arrows’ gain.
Meanwhile, after scooping the BBC award on Sunday, Hamilton expressed his delight at winning the prize for a second time in his career.
He said: “I want to say congratulations to all the incredible nominees I’m so proud of what they have achieved.
“I want to say thank you to everyone that has voted for me. I wasn’t expecting this knowing there’s so many great contenders.
“I want to say Merry Christmas to everyone – it’s been such an unusual year and I want to mention all the front line workers and all the children round the world, I want you to try and stay positive through this difficult time, I’m sending you all positivity.