The free-agency period officially opens at 1:00 on Wednesday.
Bradford will sign a deal worth $20 million for 2018 with an option year for 2019.
Mathieu's agent, Tom Condon, also represents quarterback Sam Bradford, who reportedly agreed to a one-year deal with the Cardinals on Tuesday. They turned down his request last summer for a one-year, $4 million extension.
Bradford had an outstanding 2016 season for the Vikings, but lingering knee problems as a result of previous surgeries to fix an ACL caused him to miss most of the 2017 season. He's a career 62.5 percent passer with a 1.77 touchdown-to-interception rate.
Bridgewater was expected to be Minnesota's quarterback of the future after being taken with the last pick in the first round of the 2014 draft.
The Cardinals needed a quarterback, so going for a veteran makes sense.
Bradford underwent season-ending knee surgery in November with hopes of curing ligament damage, but the procedure might not have returned him to full fitness. Case Keenum eventually assumed the role and led Minnesota to the NFC Championship Game.
After being named National Football League offensive rookie of the year in 2010, Bradford tore his left ACL in the 2013 and 2014 seasons.
Running back is another area to possibly address in the even their feature back David Johnson gets hurt again, Carlos Hyde, who is a free agent from the 49ers is a name that could be thrown around in their organization.