Lerner issued a statement confirming Haslam -- a current minority owner of the Pittsburgh Steelers -- is in the process of making "an investment" in the Browns.
"In connection with current rumors and press inquiries, I can report that I've been approached by Mr. Jimmy Haslam, who is interested in making an investment in the Cleveland Browns," Lerner said in a statement. "We are currently in negotiations and both sides have agreed to keep that dialogue and its details private.
"Given that any transaction would require League approval, care has been taken so that this process will not be disruptive to the organization, in particular the football team, as it prepares for the upcoming season. We will share further details or make an announcement if it becomes necessary."
Browns President Mike Holmgren confirmed Haslam's offer following Friday's practice.
"(Lerner) was very, very concerned with and interested in the right person stepping forward if he was going to sell the football team and apparently all the stars aligned in the last few months," he said.
Fred Nance, a senior adviser to Lerner, told the newspaper "(Lerner) has an unequivocal commitment from Haslam to never move the Browns. He made that a prerequisite before entering into negotiations."
"The Cleveland Browns aren't going anywhere," Holmgren added. "The Cleveland Browns are the Cleveland Browns and they're going to stay."
The team is tied to a 30-year lease through 2029 with Cleveland Browns Stadium and Mayor Frank Jackson has stated the city would sue if there was any attempt to break the lease and move the team.
Haslam, the president of the nation's largest chain of truckstops, is the younger brother of Tennessee Gov. Bill Haslam.