According to a source, Dick Jauron will 100% interview for the Cleveland Browns defensive coordinator position at some point in the near future. At least one other team is interested in Jauron being their defensive coordinator, but it is not as serious as the mutual interest between Jauron and the Browns.
One reason Jauron is interested in the Browns' position is obvious -- he was on Mike Holmgren's staff in Green Bay, where Fritz Shurmur was the team's defensive coordinator. Hiring Jauron would fit in with the entire staff having previous experience with each other and having the confidence that everyone could work together.
My source also notes that when Jauron was with the Buffalo Bills, he wanted to acquire Shaun Rogers badly from the Detroit Lions. Jauron really liked Rogers when he had been the Lions' defensive coordinator. The Bills had the same trade offer on the table that the Browns did for Rogers when Jauron was Buffalo's head coach, but Rogers ended up coming to Cleveland. Based on the time when Rogers felt like he was stiffed by Eric Mangini, it seems important that Rogers believes his coaches respect him. It sounds like Jauron is the type of guy Rogers would have no problems working under.