According to the website, a deal was in place that would have sent multiple draft picks to the 49ers for Harbaugh, but the coach ultimately decided not to leave San Francisco.
Sources told ESPN's Chris Mortensen that the talks reached a serious level.
Both the 49ers and Harbaugh refuted the report later Friday.
49ers CEO Jed York said in a tweet to the NFL Network and Pro Football Talk: "Is this on the record? Report isn't true."
Harbaugh told ESPN's Ed Werder via text: "I echo Jed York's comment ... 'isn't true.' I know nothing about a trade with the Cleveland Browns and us, involving me."
The Browns also released a statement Friday.
"The team conducted an extensive coaching search, and explored several options," the statement read. "That search produced an outstanding head coach in Mike Pettine, and we're excited about his future with the club."
When Pettine was hired, then-Browns CEO Joe Banner acknowledged there was one last "mystery candidate" out there who'd been under consideration but declined to name him.
Pettine called the report "noise" on Saturday and said the issue "has no bearing" on his job. The Browns didn't deny their attempt to acquire Harbaugh, but Pettine said that didn't bother him, either. He said he thought that shows the organization's commitment to turning around the struggling franchise.
The Browns, who finished 4-12 this past season after starting 3-2, have amassed picks for this year's draft, among them the fourth and 26th overall.
Harbaugh has coached the 49ers to the NFC Championship Game three years in a row, and to the Super Bowl once.
Information from The Associated Press was used in this report.