Kevin Demoff, the Rams chief operating officer, said earlier this week that Kroenke would be "heavily involved" in the search and added that the decision is "his call."
Unlike Steve Spagnuolo, who was fired Monday after going 10-38 over three seasons, Fisher offers the Rams plenty of head coaching experience. He has a career record of 142-120 and led the Titans to at least 12 wins four times.
St. Louis has also received permission to interview Cardinals defensive coordinator Ray Horton, a league source told ESPN NFL Insider Adam Schefter. The Rams plan to meet Friday with Horton.
Spagnuolo came to the Rams after success as defensive coordinator with the New York Giants.
Fisher's Titans lost to the Rams in the 2000 Super Bowl. Tennessee had the top AFC seed in 2008 with a 13-3 record but has not won a playoff game since 2004.
Some around the league believe Fisher would lean toward the Rams, if they make an offer, because they have a franchise-caliber quarterback in Sam Bradford and the No. 2 overall pick in April's draft.
Both Fisher and former Buccaneers and Raiders coach Jon Gruden have been mentioned in connection with the opening. However, Gruden, currently an analyst for ESPN, has said he is remaining with ESPN and the "Monday Night Football" broadcast team.
Fisher sat out the entire 2011 season after being fired by the Titans in January. He had served as coach of the franchise for 16 full seasons, including before the Titans moved from Houston to Tennessee.
The Rams (2-14) also are looking for a new general manager to replace Billy Devaney.
A league source told ESPN's Schefter that the Rams have requested permission to interview Indianapolis' director of player personnel Tom Telesco regarding their general manager opening. St. Louis has also requested permission to interview Cardinals personnel director Steve Keim, sources told ESPN senior NFL analyst Chris Mortensen.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was included in this report.