Winston was in the fourth year of a $30 million, five-year deal when he was cut by the Houston Texas to save salary cap space. He instantly became the most coveted right tackle on the market, and Kansas City quickly swooped in to line up a visit.
Their likely sales pitch include a chance to block for one of the most dynamic running backs in the league in Jamaal Charles, play for a team on the rise, and sample some of the world's best barbecue - Winston tweeted during his visit on Friday that Chiefs brass had taken him to Fiorella's Jack Stack Barbecue for lunch.
The 28-year-old Winston entered the league with Houston in 2006 and quickly moved into the lineup. He started every game for Houston over the past five seasons.
Winston will take over at right tackle for Barry Richardson, who struggled much of last season before becoming a free agent.
"Hello, Kansas City!" Winston tweeted Saturday night. "Anyone know where some good neighborhoods to live in?"
Quinn was targeted to backup quarterback Matt Cassel, who will be coming back from a season-ending injury to his throwing hand.
The former first-round pick of the Browns started 12 games over three seasons in Cleveland, completing 52 percent of his passes for 1,902 yards and 10 touchdowns with nine interceptions. He did not play as a backup last season in Denver.
The Chiefs have been aggressive in upgrading an offense that ranked among the last in the league in nearly every significant statistical category last season.