Family business Hulman & Company, which owns US car-racing series IndyCar, has no current plans to replace family member Tony George from the firm's board, following his surprise resignation last week.
George quit the board on 19 October after citing a conflict of interests over his attempt to take over the IndyCar series.
A spokesman for the company told CampdenFB: "I don't know if there will be a replacement."
Rumours that 52-year-old George wanted to buy the auto-racing sanctioning body, which he founded in 1996, had been circulating for months. According to the latest reports, he also recently submitted a purchase proposal for IndyCar.
“I realise that my recent efforts to explore the possibility of acquiring IndyCar represent the appearance of a conflict, and it is in everyone's best interest that I resign," he said in a statement.
In a separate announcement, Hulman president and chief executive Jeff Belskus insisted that IndyCar was not for sale.
"While the business is not for sale and no offers to sell it have been considered or are being considered, we applaud Tony's efforts to resolve the appearance of a conflict and appreciate the gravity of this decision," he said.
He added: "Tony has been involved with our businesses for many years and has contributed significantly through his leadership role with IMS [Indianapolis Motor Speedway] and IndyCar and as a member of this board."
George served as chief executive of IndyCar from 1994, but was ousted by his mother and sisters in 2009. He was also president of IMS, also owned by the family, from 1990 to 2009 and is now co-owner of Ed Carpenter Racing with his stepson, driver Ed Carpenter.
His mother, Mari Hulman George, and his sisters, Nancy George, Josephine George and Katherine George-Conforti, will continue to serve as members of the 10-strong Hulman board.
The company, which also owns Clabber Girl Corporation and other affiliated companies, was founded in 1850 by Francis Hulman as a wholesale grocery, tobacco and liquor business in Terre Haute, Indiana.