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The interview will take place in the New England area.
Under league rules, only assistants with teams that earned byes in the first week may interview for vacant head coaching positions. Under league policy, teams seeking a head coach may interview bye-week candidates but are not allowed to offer them a job or engage in negotiations until that team is finished with its postseason.
Cleveland is looking to replace Rob Chudzinski, who was fired after going 4-12 and finishing on a seven-game losing streak in his only season as head coach.
The Browns also have asked permission to interview three assistant coaches: Arizona Cardinals defensive coordinator Todd Bowles; Seattle Seahawks defensive coordinator Dan Quinn, who can interview Sunday, a source told ESPN NFL Insider Adam Schefter; and Denver Broncos offensive coordinator Adam Gase, who also will interview.
Gase would prefer to wait until after the Broncos are eliminated from the playoffs before speaking with anyone, however.
Jim Schwartz, fired earlier this week as head coach of the Detroit Lions, also could be interviewed.
The Browns still owe Chudzinski $10.5 million, league sources told Mortensen.