Schaffer made the announcement just hours after Reps. Scott McInnis (search) and Tom (search) Tancredo joined a growing list of Republicans who declined to run. Schaffer said a formal announcement would come next week.
"I've filed and I have an organization that I've put together, an exploratory team and a team that is getting larger," he said. "I see nothing that discourages me."
Schaffer was elected to the House of Representatives in 1996 and served three terms, stepping down to fulfill a self-imposed term limit pledge.
GOP Gov. Bill Owens, Rep. Bob Beauprez and state Treasurer Mike Coffman previously said they would not seek the Republican nomination.
Campbell's announcement and Owens' decision not to run have boosted Democrats' hopes of making up lost ground in Colorado as they try to retake control of the U.S. Senate. Republicans hold a 51-48 majority with one Democrat-leaning independent.
Other potential GOP candidates include Lt. Gov. Jane Norton and Jim Nicholson, the chairman of the Republican National Committee from 1997 to 2001.
Campbell, 70, announced abruptly last week that he would not seek re-election, citing his health. He was treated for prostate cancer last year. His Washington office also faces allegations that a longtime aide had taken kickbacks.