Munchak was fired earlier this month by the Titans after going 7-9 in his third season with Tennessee. He also has interviewed for the Detroit Lions' head coaching vacancy, the Houston Texans' offensive line coach position and the head coaching job at his alma mater, Penn State.
A Hall of Fame offensive lineman, Munchak spent 31 years as either a player or a coach with the Titans franchise.
League sources told ESPN that Munchak declined the Titans' offer of a multiyear contract extension contingent on more than a dozen firings and demotions on his coaching staff.
Cleveland is seeking a replacement for Rob Chudzinski, who was fired after going 4-12 in his only season as head coach.
The Browns already have been spurned by New England Patriots offensive coordinator Josh McDaniels, who withdrew his name from consideration last week.