The 6-foot-6, 230-pound Walter has spent the last four seasons with Oakland after being selected by the Raiders in the third round of the 2005 draft out of Arizona State. He has played in 15 games, starting nine, and completed 174 of 333 passes for 1,919 yards and three touchdowns.
He was waived by the Raiders on Thursday.
Gutierrez joined the Patriots as a rookie free agent out of Idaho State in 2007. He played in five games as a rookie, completing one pass for 15 yards. He began last season on the practice squad before being signed to the 53-man roster on Sept. 13 following a season-ending knee injury to Tom Brady.
The Patriots had brought in quarterback Cleo Lemon for a workout on Saturday and were reported to be considering signing him. Lemon is a 29-year-old veteran who has played for the Baltimore Ravens, San Diego Chargers, Miami Dolphins and Jacksonville Jaguars.
Information from The Associated Press was used in this report.