Shurmur will be the first candidate to formally interview with the Browns. The 45-year-old previously worked in Philadelphia with Cleveland's general manager, Tom Heckert, who along with team president Mike Holmgren will handle interviews.
The Browns are expected to meet Saturday with Atlanta Falcons offensive coordinator Mike Mularkey. The former Buffalo Bills coach canceled his Friday interview with the Denver Broncos because he doesn't want to take too much time away from his preparation for next week's playoff game.
Holmgren, who fired Eric Mangini on Monday after two losing seasons, also has asked for permission to speak with New York Giants defensive coordinator Perry Fewell, who reportedly interviewed for the Carolina Panthers' head-coaching job Thursday.
The Associated Press contributed to this report.