"I'm sure he's a guy we'll take a peek at and we kind of have a rapport with," Veach said, according to Adam Teicher of ESPN.
Veach and Chiefs head coach Andy Reid were with the Philadelphia Eagles when they drafted McCoy in 2009. Reid spent four seasons as McCoy's head coach in Philadelphia before moving on to Kansas City in 2013, which was the same year Veach joined the Chiefs.
McCoy spent the past four seasons in Buffalo. Last year, he registered career lows in rushing yards (514) and yards per carry (3.2) and hauled in 34 catches (the third-lowest mark of his career) for 238 yards (second-lowest). He was limited to 14 games because of rib and hamstring injuries.
Prior to last season, he had earned five consecutive Pro Bowl nods.
Kansas City could be in the market for an established running back after cutting ties with Kareem Hunt last season. The Chiefs signed Carlos Hyde to a one-year, $2.8 million deal in March, but that experiment ended Saturday when they traded the veteran to the Houston Texans.
As a result, Damien Williams (who has never had more than 50 carries in any of his five seasons) sits atop the depth chart. Second-year back Darrel Williams and rookie Darwin Thompson are slated to serve as his backups.
Though the 31-year-old McCoy is coming off a down year, he is familiar with Reid and has performed well under him. And as the Times-Picayune's Herbie Teope noted, McCoy once said Reid "is like family to me."