The two parties are currently renegotiating his deal, and looking to put a long-term contract in place rather than simply take up the one-year extension.
Whitmarsh, who was talking in an interview with 5 Live, was asked whether a four or five year contract might happen.
He said that sort of time period would be the case in "an ideal world".
JENSON BUTTON: THE FACTS
2009 world champion with Brawn GP
Moved to McLaren for 2010
Four wins since joining: Australia & China in 2010, Canada & Hungary in 2011
Fifth in championship last season, 4th so far in 2011
Has 11 career wins overall
He added: "The nature of a contract is not something we are going to talk about publicly.
"We're just talking about it [at the moment]. I don't think there's any rush to go to a single year contract.
"Jenson's done some of the most spectacular drives in the history of Formula 1 this year. And I think he's capable of even more."
Button's team-mate Lewis Hamilton has one year to run on his McLaren contract, which expires at the end of 2012.
His options elsewhere are limited.
Fernando Alonso, with whom Hamilton spent a tumultuous season at McLaren in 2007, is committed to Ferrari until the end of 2016, and the team are unlikely to want to destabilise him by signing Hamilton.
The Englishman sought out Red Bull team principal Christian Horner at the Canadian Grand Prix in June to discuss the future, although it is understood they did so only in the loosest terms.
Their second seat alongside world champion Sebastian Vettel is up for grabs at the end of next season, with Mark Webber committed only to a one-year deal.
But Horner has sounded lukewarm on the prospects of a Hamilton-Vettel partnership, saying he had concerns over whether it could destabilise the team.
Listen to the full interview with Martin Whitmarsh on 5 live F1 at 2130 on 909 and 693 MW
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