Fallon is expected to snatch the $230m Gateway Computers account after incumbent McCann Erickson was sacked earlier this week.
Gateway will not confirm a pitch-list but admitted it was in discussion with a number of agencies about its advertising requirements after it announced the split with McCann.
Manager of consumer initiatives Greg Lund said: "It's an amicable parting. We wish them well, and need to assess our brand and continue building it in new ways."
McCann will continue to work on the account until a new agency is appointed. The Gateway executive who awarded the agency the account shortly after he arrived at the company in January 1998, Jeffrey Weitzen, resigned as president and ceo two weeks ago. Gateway founder Ted Waitt has since taken on his responsibilities.
Universal McCann will continue to handle planning and buying duties for Gateway.