"Your QB could never," the Browns tweeting, sharing a video filmed for the Madden video game.
The video featured Mayfield dancing in his jersey to Swift's Shake It Off. Mayfield followed the dance with a one-handed catch, before he started dancing once again. The second performance came with Migos' Walk It Talk It playing in the background.
Foster corrected the Browns' caption, saying his quarterback "*would never" do what Mayfield did in the video.
"Respected you before this," Mayfield tweeted back to Foster. "I get it dog, you're too cool to show any personality. Everybody's different, though. No need to speak on it."
Foster later responded to Mayfield, sending him a link to the book The Four Agreements: A Practical Guide to Personal Freedom.
Foster, 32, was a four-time Pro Bowl selection and a 2010 All-Pro during his eight-year NFL tenure. He played his final season in 2016 for the Miami Dolphins.
Mayfield was a member of the 2018 NFL All-Rookie team after completing 63.8 percent of his passes for 3,725 yards, 27 touchdowns and 14 interceptions in 14 games for the Browns.