The bosses of the McLaren and Renault teams believe the threat of a breakaway series in 2008 is all but over.
Dennis says a compromise deal is close
They are two of the five teams who have so far refused to commit to F1 beyond the 2007 season in a row over money and the way the sport is governed.
But McLaren boss Ron Dennis said: "I think everyone in F1 will be in F1 in 2008 on the basis of this issue."
"I believe we are quite close to a commercial deal," his Renault counterpart Flavio Briatore said.
"We are basically agreed. Something will happen maybe this week or next week, but on the commercial part I believe we are very much in agreement."
Both men were talking about the proximity of a commercial deal with F1 supremo Bernie Ecclestone.
Dennis also predicted compromise over technical issues, and said: "If Formula One exists we want to be in Formula One.
"We are not going to put ourselves in a position where we don't compete."
Dennis predicted all issues would be resolved in "more than a day but less than a month."
The rebel teams formed the Grand Prix Manufacturers' Association to champion a rival series.
But Dennis said there is a "positive desire" to find a solution both with Ecclestone and FIA president Max Mosley.
Mosley wants radical rule changes to cut costs, but the five teams are keen to maintain Formula One's hi-tech image.
"It is important to remember that we are talking about 2008," Dennis added added.
"In any process there has to be compromise at the appropriate time. That appropriate time we recognise as now.
"Everyone involved is determined to take decisions on the basis of what is best for Formula One."
And he rejected claims that the basis for the dispute was financial.
"I think everybody understandably forms the view that everything is about money and of course money is so often talked about in Grand Prix racing," he said.
"But what is important to understand is that this embraces the future of Grand Prix racing through to at least 2012 and maybe beyond."
He said the carmakers were working on a wide-ranging memorandum of understanding.
"I think the difference in the discussions that have taken place in the last month... is that the push now is more towards what is in the long term interests of Formula One," said Dennis.
"That is where probably the acquisition from the banks of the equity by CVC has been most positively felt because they want stability, they want growth and now we participate in that growth so everybody has a very common interest."
CVC Capital Partners have taken control of F1's commercial rights after buying the stakes of two of the three banks that owned 75% of holding company Slec through Speed Investments.
An anti-trust review of that takeover is being carried out by
the European Commission with a decision expected by 21 March.