Two NFL executives told ESPN's Chris Mortensen they believe Edwards will be claimed on waivers by 4 p.m. Tuesday.
The Carolina Panthers, Jacksonville Jaguars, Kansas City Chiefs, New York Jets, San Francisco 49ers and Seattle Seahawks are among the teams expected to put in a claim.
Edwards was in his fourth season after being selected by the team in the third round of the 2007 draft and eventually replaced J.P. Losman midway through his rookie season. He went 14-18 as a starter.
Teams 2009 records are determined when deciding who has first priority, which would mean the Cheifs are first in line.