With the play of rookie Patrick Mahomes II in training camp, it was thought that the Chiefs would have entertained offers for Smith this summer, but no team stepped up to make a deal happen.
Smith has said that he thinks this will be his last year in Kansas City. With many quarterback-needy teams around the league, he likely would be in high demand if made available in a trade.
Smith, 33, is under contract through the 2018 season and is scheduled to make a base salary of $14.5 million next season. He was named the AFC Player of the Week in Week 1 after throwing for 368 yards and four touchdowns in the Chiefs' 42-27 road victory over the New England Patriots in the NFL season opener.
The Chiefs paid a heavy price to trade up to select Mahomes in the 2017 draft, sending the No. 27 pick in the first round, a third-round pick and their 2018 first-round selection to move into the No. 10 spot to pick Mahomes.