They expect their driver to stay, probably making a decision within the week, even though the new offer is still short of what Hamilton is currently paid.
The anticipated success is why McLaren executives left Singapore on Sunday looking a little more relaxed than they were entitled to after Hamilton retired on the 23rd lap when in the lead. It could have been his third victory in four outings but the retirement dropped him from second to fourth in the championship table, where he trails Fernando Alonso by 52 points.
McLaren, though, believe they have won the more important competition to secure the services of Hamilton over the next three years. His existing contract, which ends in November, is often reported to be £75m over five years, or £15m a year, but is believed to be a little less than that.
According to sources at McLaren, the money on offer from Mercedes is not as substantial as the £20m a year that has been reported. It is fair to say that Mercedes, who hold a board meeting on Wednesday, have been prepared to match McLaren's terms, with more money on offer through image rights. Mercedes pay Michael Schumacher, who at 43 has failed to finish seven of his races this year, £16m.
The deal to secure Hamilton is still not complete and, according to the Formula One commercial rights holder, Bernie Ecclestone, Hamilton had at one point decided to join Mercedes.
Ecclestone said on Monday: "I don't think Hamilton knows what he will do. These last couple or three races he has been doing very well. Before that, why he was upset I don't know but he was definitely going to move no matter what. He had made up his mind that he was going. Whether he has changed now I don't know."
Many at McLaren had also concluded their driver was to switch to Mercedes but Hamilton has been impressed by the renewed competitive qualities of the car that until Sunday's breakdown saw him emerge as Alonso's strongest challenger. McLaren, with whom Hamilton won his only world title in 2008, have won more races this season (five) than any other team. Moreover, there are no opportunities at the other two big teams, Ferrari and Red Bull.
Jenson Button, second in Singapore but out of the championship race, said that McLaren are throwing away points. "It was not a bad result for me personally but I am sure that the team is disappointed."
Button, who failed to finish the previous race in Italy because of fuel pump problems, added: "The team is doing such a good job in every other area. Two failures in two races is not what McLaren is about. We have to solve these issues. The pace is there, so that is why it's tough, because we're throwing away a lot of points. That's 43 points we have lost [in two races]."
Despite an impressive run of form – McLaren have won four successive poles for the first time since 1999 and almost made it four wins in a row – Button, surprisingly, feels his team are still playing catchup. "I don't think we have the best car. We are very strong in qualifying but Red Bull have good pace. They will be very competitive now. Fernando has not just got the McLarens too worry about, he has the Red Bulls and that makes it tough for him. But he has a 29-point advantage."
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image: © McLaren