McClain was a rotational defensive tackle for the Falcons last season and would be looking at a similar role in Arizona.
McClain, 30, is a former third-round pick of the Panthers back in 2011. He lasted just over a year in Carolina before he was waived at the start of the 2012 season and later signed by the Patriots.
McClain later caught on with the Texans and spent two years in Houston before the Cowboys signed him to a three-year contract in 2014.
The Redskins gave McClain a four-year, $21 million contract in 2017. He was set to make base salaries of $3.25 million and $4 million over the next two years of the agreement when Washington released him after only one year.
In 2018, McClain signed a one-year, $4 million deal with Atlanta.
In 2018, McClain appeared in 13 games for the Falcons and recorded 17 tackles, one tackle for loss and one sack.