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.
Harbaugh has coached the 49ers to the NFC Championship Game three years in a row, and to the Super Bowl once.
"The team conducted an extensive coaching search, and explored several options," the Browns said in a statement Friday. "That search produced an outstanding head coach in Mike Pettine, and we're excited about his future with the club."
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."
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.
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.