Schefter reported Thursday that McCoy was likely to become the backup to Cardinals quarterback Kyler Murray following a visit with the team that was set for this week.
McCoy appeared in four games and made two starts for the New York Giants last season, throwing for 375 yards and a touchdown on a 60.6 completion percentage. He threw one interception and was sacked five times.
The 34-year-old had two solid seasons as a starter at the beginning of his career, when the Cleveland Browns drafted him in the third round in 2010. The Texas product slotted in as the starter for eight games as a rookie and then made 13 starts in 2011. Overall, he led the Browns to a 6-15 record throughout those two seasons.
In 2011, he threw for 2,733 yards and 14 touchdowns, but he was picked off 11 times and sacked on 32 occasions.
He has spent the bulk of his career in Washington, where he appeared in 12 games over five seasons.
The Cardinals are set under center with Murray, who followed up his Offensive Rookie of the Year campaign in 2019 with a Pro Bowl selection last season. Murray fell just short of the 4,000-yard mark, finishing with 3,971 passing yards and 26 touchdowns with 12 interceptions. He also added 819 yards and 11 touchdowns on the run.
He provides another option for the Cardinals over Chris Streveler, who appeared in five games last season behind Murray.