Williams is searching for a new title sponsor after communications company AT&T's deal with the Formula One team ended.
Dallas-based AT&T, which runs the second-largest wireless network in the United States, was Williams' main sponsor for five years until the contract ended last month.
Williams says "both parties decided not to renew for 2012."
The British team has won 113 Grand Prix races, nine constructors' championships and seven drivers' titles. But its last victory was at the 2004 Brazilian Grand Prix, and it hasn't won a drivers' or constructors' title since Jacques Villeneuve won the championship in 1997.