Whitmarsh insisted he was not putting on a brave face, however at no stage did he deny Hamilton would be leaving the team at the end of the year.
Instead, Whitmarsh maintains the focus from the team and Hamilton is on winning this year's drivers' and constructors' titles, suggesting the debate over whether Hamilton stays or goes to Mercedes is merely a sideshow.
Press Association Sport learned this week Hamilton has two contract offers on the table from McLaren and Mercedes, with the ball in his court as to where he decides to go.
Asked whether he accepted Mercedes had offered Hamilton a deal, and with reference to Caterham owner Tony Fernandes sat alongside him, Whitmarsh smiled and said: "I suspect Tony has made him an offer as well. He is a very good racing driver."
A non-plussed Fernandes simply replied: "I haven't."
Whitmarsh conceded after Hamilton's win in the Italian Grand Prix 12 days ago there was "no plan B" in terms of finding a replacement.
Although Sauber's Sergio Perez has been linked of late, Whitmarsh again denied there had been any consideration towards a replacement.
"No," said Whitmarsh. "We're focused on trying to do a very good job here.
"The speculation is not a distraction. The last three races we have got stronger and more focused.
"Anyone who knows Lewis has witnessed, in Italy and here in Singapore so far, he is very focused on doing a job.
"He realises this year we have a strong opportunity to win a world championship, with our focus to improve the car, not to make mistakes and maximise the points we get from each race.
"I know there are stories and speculation swirling around, but that's Formula One, and we're content to get on with our job quietly."
Pointedly asked whether McLaren were looking to pay Hamilton less, and it is understood the new deal involves a pay cut of a third on his current £10million-per-year contract, Whitmarsh again dodged the question.
"I'm sure he'll want more money and I'm sure we'll want to pay less, that's how business normally works," said Whitmarsh.
Given the levity of some of Whitmarsh's replies, it led to him being asked whether he had seriously given thought to life without Hamilton from next year.
"It's not a question of putting on a brave face, it's a question of focusing on doing our job," he replied.
"We're concentrating on this year's championship, and speculation on next year is something we don't need to entertain or respond to.
"We're focusing on the here and now."
Which prompted the suggestion McLaren could even wait until the end of the year to make an announcement over Hamilton to which Whitmarsh said: "We might wait until then. You never know."
From the outside looking in it appears as if Hamilton and McLaren have dragged out the whole contract affair given there remains no resolution, even though the team knew this situation would arise.
But Whitmarsh said: "It seems a long time because of the speculation people have made.
"But when you sit down and seriously put your mind into entering into a new contract it doesn't take too long.
"It's a question of priorities and other things we've been doing."
Given Hamilton put a block on questions yesterday [Thursday] with regard to his future, it is clear he and McLaren are adopting a siege mentality and have closed ranks.
As far as they are concerned, with the titles on the line, they are the goal.
After winning two of the last three races, Hamilton has closed to within 37 points of title leader in Ferrari's Fernando Alonso.
With the team winning the last three races overall given team-mate Jenson Button triumphed in Belgium, McLaren are 29 points behind Red Bull in the constructors' championship.
The suggestion McLaren are favourites was one Whitmarsh, rightly on this occasion, expressed caution over.
"We were firm favourites going into the season and firm favourites coming out of Australia (after Button's win), but it can change," said Whitmarsh.
"We're very pleased we've been competitive at the last three events on very different circuits.
"What we haven't done is piled on the points as we should given the competitiveness of our car.
"We've clearly a strong package so we should be disappointed with the points we don't have rather than the points we do.
"But you don't look back, you look forward, and we're hopeful of getting a result here to keep the pressure on."