On Thursday, Browns offensive coordinator Freddie Kitchens said he did not have any issues with Mayfield's recent public statements about Jackson and an Instagram comment calling Jackson "fake."
"I promise you this, Baker's not going to blow smoke up anybody's [butt]," Kitchens told reporters as the Browns continued their preparations for Sunday's visit to the Houston Texans. "So if he said it, that's what he feels and I'm standing behind Baker Mayfield."
Jackson was fired by Cleveland on Oct. 29 after posting a 3-36-1 record in two-plus seasons with the team. He joined the Bengals as a special assistant to head coach Marvin Lewis on Nov. 13.
After last week's 35-21 win at Cincinnati, Mayfield said he did not appreciate Jackson taking a job with a division rival after being fired two weeks earlier.
"I don't have a problem with Baker saying anything like that," Kitchens said. "The guy spoke what he felt to be true. I don't know when it became big news to speak the truth, OK? And if that's what he feels then he should voice it."
On Wednesday, Mayfield admitted he called Jackson "fake" but declined to explain the reason for it.
"There were just things that happened inside the building that I'm not going to get into detail with," Mayfield said. "It's in-house information."
In three games since Jackson and offensive coordinator Todd Haley were fired, the Browns have won twice and Mayfield has completed 74 percent of his passes with nine touchdowns and complied a quarterback rating of 129.5.