The Browns have also asked for permission to interview Denver Broncos offensive coordinator Adam Gase and Seattle Seahawks defensive coordinator Dan Quinn, according to other reports.
Several other candidates could be on the Browns' radar, including two college coaches - Auburn's Gus Malzahn and Vanderbilt's James Franklin.
Malzahn has the Tigers in the BCS championship game in his first season as head coach and Franklin has had success at Vandy as well as NFL experience with Green Bay as an assistant.
The Browns also reportedly sought permission to interview Cardinals defensive coordinator Todd Bowles, who would satisfy the NFL's Rooney Rule.
The 37-year old McDaniels, who has a longstanding relationship with Cleveland general manager Mike Lombardi, grew up rooting for the Browns in his hometown of Canton, Ohio.
"Josh is the best offensive coach I could ever imagine," quarterback Tom Brady told WEEI-FM on Monday. "He's so prepared; he's so confident in what he does. He figures out a way every week to get us in the best position as players to win. I have so much respect for him and what he does for me, what he does for our team. He's just a great coach."
McDaniels was fired as head coach of the Denver Broncos in 2010 after losses in 17 of his final 22 games in Denver.
Rob Chudzinski was fired Sunday night by the Browns after just one season as head coach.
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There is no guarantee that Geno Smith will keep the starting quarterback job with the New York Jets next season after starting all 16 games in 2013.
Smith completed his rookie season in the NFL as the team's starter with mixed reviews, but general manager John Idzik has stopped short of committing to Smith for 2014.
The Jets finished 8-8 after season-ending wins over the Cleveland Browns and Miami Dolphins. Smith passed for 3,046 yards with 12 touchdowns and 21 interceptions and also rushed for six touchdowns in his first season.
The future of veteran quarterback Mark Sanchez remains unclear, but he is expected to be released during the offseason because he carries a $13.1 million cap hit for 2014. Sanchez missed the 2013 season with a shoulder injured suffered during the preseason.
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Whether it's a job with the Philadelphia Eagles or another team, Michael Vick wants to play in the NFL next season.
The 33-year-old quarterback said he would like to start for a team in 2014 but would be willing to return to the Eagles as a backup to starter Nick Foles if no other jobs materialise during the offseason.
Vick suffered a hamstring injury in October and lost the Eagles' starting job to Foles. Vick finished the season with 1,215 passing yards, 306 rushing yards, five touchdown passes, three interceptions and two rushing scores in seven games.
Injuries have kept Vick from playing a full season since 2009.
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A wrongful death suit seeking unspecified damages has been filed against the Kansas City Chiefs by the mother of Jovan Belcher.
The former linebacker killed his girlfriend and himself in December 2012.
The suit alleges Belcher showed signs of cognitive and neuro-psychiatric impairment and that he "unknowingly sacrificed his brain" during his four years with the team, The Kansas City Star reported.
Two weeks ago, Belcher's family requested that his body exhumed in order to have his brain studied for chronic traumatic encephalopathy (CTE). The results are pending. CTE is mentioned throughout the suit.
Belcher, 25, shot and killed his girlfriend, Kasandra Perkins, on December 1, 2012, and then drove to the Chiefs' practice facility before he shot himself in the head.
The Star reported that there was no history of concussions or head injuries, but the suit contends that the Chiefs missed signs of head trauma and the team "directly caused or directly contributed" to his neurological problems.
The suit also alleges the team "engaged in mental abuse to motivate" Belcher to play through injuries and that it "caused or contributed to cause (him) to become insane."
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Kansas City Chiefs wide receiver Dwayne Bowe has received the go-ahead to play Saturday in an AFC wild-card game against the Indianapolis Colts, but rookie right tackle Eric Fisher did not practice on Tuesday and might miss the play-off opener.
Bowe sat out the Chiefs' regular-season finale against the San Diego Chargers because of a concussion. He returned to practice on Tuesday.
Bowe had 57 receptions for 673 yards and five touchdowns during the season.
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Baltimore Ravens offensive coordinator Jim Caldwell will interview for head-coaching openings with the Detroit Lions and the Washington Redskins, according to reports.
The Redskins are searching for a replacement for Mike Shanahan, who was fired earlier this week after four seasons as their coach. The Lions ousted coach Jim Schwartz on Monday after five seasons.
Caldwell helped the Super Bowl-winning Ravens last season when he stepped in to replace Cam Cameron as offensive coordinator.
Before Caldwell joined the Ravens, he led the Indianapolis Colts to Super Bowl XLIV, where they lost to the New Orleans Saints after the 2009 season.
Caldwell, who served as coach Tony Dungy's quarterbacks coach and assistant coach for seven seasons, was fired by the Colts after posting a 26-22 regular-season record in three seasons, including a 2-14 mark in 2011 without Peyton Manning at quarterback.
The Redskins' interview list includes Seattle Seahawks offensive coordinator Darrell Bevell and Carolina Panthers defensive coordinator Sean McDermott, according to reports.