NFL Network's Ian Rapoport reported the Chiefs would be open to moving Smith, though they aren't going to actively seek out trade partners.
Mahomes started Kansas City's Week 17 game over the Denver Broncos after the team had already clinched the AFC West title. The rookie quarterback went 22-of-35 for 284 yards with no touchowns and one interception in a 27-24 victory.
John Dorsey, who was Kansas City's general manager when the team acquired Smith from the San Francisco 49ers in 2013, was named the Browns general manager last month. Carson Palmer retired earlier this week after 15 NFL seasons, including the last five with the Cardinals.
Smith is signed through 2018 with a $20.6 million salary-cap hit, per Spotrac. The 33-year-old threw for a career-high 4,042 passing yards and 26 touchdowns this season.