It had emerged last month that only Ferrari and Red Bull had been offered the special deals for the new Concorde Agreement, including the right to nominate directors for the sport's holding company.
But new reports on thisismoney.co.uk and in the Daily Mail, by the respected F1 business news writers Christian Sylt and Caroline Reid, say McLaren has also been given a seat on the board by F1 chief executive Bernie Ecclestone.
The report said the move could "dilute opposition" to Ecclestone's plans to float formula one on the Singapore stock exchange.
Sources said the floatation plans must be approved by the board.
Ecclestone told Germany's Auto Motor und Sport this week that it was his suggestion that F1 be floated in Singapore, not in London.
"Formula one is known in Singapore, and Asia is thriving. It is a simpler market and not as restrictive," he said.
The 81-year-old said just a year ago that F1 would never float whilst under his control, because "there's no way I would sit in front of a load of shareholders".
"Let's wait and see," he now insists.
"Shareholders are always happy when they're making money. As long as we can guarantee that, they will leave us in peace."