The 29-year-old Briton, who can become a double world champion at Yas Marina, has a year remaining on his current deal but Mercedes are looking well beyond that.
“We want him very much to stay for many more years,” Mercedes motorsport head Toto Wolff told reporters ahead of the season-ending race.
“He’s great for the team, he’s part of the family, the relationship we all enjoy is more than just a professional racing relationship between driver and team. It’s on a different level.”
Hamilton has a 17 point lead over German team mate Nico Rosberg but an unprecedented double points on offer in Abu Dhabi means there is everything to play for.
Rosberg, winner of five races this season to Hamilton’s 10, agreed a multi-year contract extension in July.
Wolff said Mercedes had agreed to defer talks with the Briton until after the final race so he could concentrate on his driving.
“We did that very consciously even when the rumours accelerated around other drivers and our team. We sat down again and said “Should we maybe take those conversations forward?” and we decided ‘No, it’s not the best thing to do’.
“And so on the Monday or Tuesday after Abu Dhabi we will sit down and discuss and hopefully find a solution quickly.”
Ferrari’s Fernando Alonso, the double world champion who is set to join McLaren next year when they start a new partnership with Honda, has made little secret of his interest in moving to Mercedes in 2016.
However the Spaniard’s overtures appear destined to be rejected, unless 2008 champion Hamilton decides to go elsewhere.
Wolff said Hamilton, who has let a management deal with XIX Entertainment lapse, was perfectly capable of negotiating his own deal.
“Lewis is a very intelligent and mature person now who knows more about Formula One than many other managers out there,” he said. “I think he can represent himself in a good way, he has good support from consultants he needs to have, be it legal or tax or whatever.
“He knows what he wants and is straight about it.”
(Reporting by Alan Baldwin, editing by Justin Palmer)