Mayfield has been given the nod as the Panthers' starting QB after a prolonged battle with Sam Darnold to start the 2022 NFL season.
Mayfield's exit from the Browns, who took him with the first pick in the 2018 NFL Draft, occurred after they traded for quarterback Deshaun Watson.
As a result, Mayfield requested that the Browns trade him, joining the Panthers in July, although he has been reluctant to criticise his former franchise publicly.
NFL Network analyst Cynthia Frelund claimed on Monday night's Around The NFL podcast that Mayfield echoed the remark to her, albeit innocuously, after last week's preseason finale against the Buffalo Bills.
"First, I didn't say it," Mayfield told reporters. "Everybody is going to write whatever story they want.
"There's history because I played there the last four years. I'm an extremely competitive person. Everybody knows that. If I wasn't wanting to win, then there would be a really big issue of me being the quarterback here.
"I want to win in everything I do. That'll never change. But it's not how I phrased it. It's not even what I said, so let's leave it at that."
He added: "I didn't even say anything. All I did was, 'Great, hope we win.' Pretty plain and simple. I'm competitive. I want to win. I don't think that should be harped on.
"That's the extent of it. It's obviously a bigger story because I haven't given the media what they've wanted me to give them this year in this offseason."
Mayfield conceded that the season opener against his former side meant something to him although he did try to downplay the narrative.
"Obviously, there's a lot of attachment there," he said. "I'm not going to sit here and be a robot and say it doesn't mean anything. It will.
"It's a great storyline. It really is because I wasn't expected to be out of Cleveland. But after Week 1, there's 16 more that really, really matter. That's how I'm approaching it."
Mayfield started 59 games in his four seasons in Cleveland and helped lead the Browns to their first playoff victory since the 1994 season in 2020. The QB went 29-30 in 59 regular-season starts with the Browns.