NFL.com earlier had news of the interview.
Considered an innovator with his passing schemes, Martz was architect of the "Greatest Show on Turf" while with the Rams, who won the Super Bowl after the 1999 season with him serving as offensive coordinator. He was named the team's head coach before the 2000 season and went 53-32 in five seasons at the helm.
Martz in many ways would represent a 180-degree turn from what Browns coach Mike Pettine said he wanted last season -- a team that would run the ball and throw off the run. Martz's emphasis is on the passing game.
Martz is the latest name to surface in a thorough search that has cast a wide net, as numerous names have been connected to the job. They include several who have interviewed or will this week at the Senior Bowl: former Bears coach Marc Trestman, Raiders quarterbacks coach John DeFilippo, New York Jets running backs coach Anthony Lynn, former Bears quarterbacks coach Matt Cavanaugh, Raiders senior assistant Al Saunders, former Buffalo Bills and Dallas Cowboys coach Chan Gailey, and Browns tight ends coach Brian Angelichio.
The Browns also are expected to interview former Jets and Eagles coordinator Marty Mornhinweg this week at the Senior Bowl, according to a source. Mornhinweg coordinated Andy Reid's offense in Philadelphia from 2006-12 and the Jets with Rex Ryan from 2013-14.
Three others the team reportedly was interested in talking to took other jobs: Scott Linehan stayed with the Cowboys, Bill Callahan went to Washington and Greg Roman joined the Bills.
The Browns are replacing Kyle Shanahan, who resigned after one season in Cleveland with two years left on his contract.
ESPN.com's Jeremy Fowler contributed to this report.