Formula One's governing body has invited tyre makers to tender for the right to become the sport's sole supplier for three years from 2008.
The International Automobile Federation (FIA) said in a statement on Monday that all bids must be submitted formally by June 23.
Formula One already have a sole supplier next season, with Japan's Bridgestone on their own after French rivals Michelin announced last year that they were pulling out at the end of 2006.
Bridgestone, long-term partners to Ferrari, were also sole suppliers in 1999 and 2000 after Goodyear withdrew and have said they want to continue.
The FIA and teams want a single supplier to help reduce costs, because most testing is tyre-related, and create more of a level playing field.