The Kansas City Chiefs are expected to listen to trade offers for quarterback Alex Smith after this season, according to league sources.

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.

Alex Smith threw for 368 yards, including four touchdown passes, in the Chiefs' season-opening win. Maddie Meyer/Getty Images

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.

On Sunday, Smith was 21-of-28 for 251 yards and one touchdown in a 27-20 win over the Philadelphia Eagles.

The Chiefs paid a heavy price to move up to the No. 10 spot in the 2017 draft to select Mahomes, sending the No. 27 pick in the first round, a third-round pick and their 2018 first-round selection to the Buffalo Bills.