Lamonte didn't return numerous phone messages left by The Associated Press with his agency.
Although he lacks head-coaching experience, Shurmur's background running a West Coast offense and working with young quarterbacks appeals to Holmgren, who started his search determined to "find exactly the right person for the job who can eventually someday lead us to the championship. That is my only goal."
Holmgren wants to expand the Browns' offense, which languished under coach Eric Mangini and offensive coordinator Brian Daboll. Mangini was fired earlier this month after two 5-11 seasons.
The Browns met with two other head-coaching candidates, Atlanta Falcons offensive coordinator Mike Mularkey and New York Giants defensive coordinator Perry Fewell, over the past week. It also was assumed that the Browns would interview Eagles offensive coordinator Marty Mornhinweg, but that meeting never took place.
The Associated Press contributed to this report.