Fisher has yet to notify either team, but sources told Lombardi a decision could come Thursday.
One of the issues holding up a deal between Fisher and the Rams is compensation, league sources told NFL Network insider Jason La Canfora. Fisher is seeking to be among the higher-paid coaches in the league, in the range of $7 million per season, the sources told La Canfora. But Rams owner Stan Kroenke hasn't displayed a willingness to reach that stratosphere to this point, the sources said.
According to La Canfora, Fisher likely will command a title of executive vice president wherever he lands. In Miami, that title would trump that of general manager Jeff Ireland, which would shift the organization's current structure. Dolphins owner Stephen Ross is believed to be willing to spend to a higher threshold in order to land Fisher, sources said.
Sources also have indicated to Lombardi that Fisher isn't interested in a potential relocation and feels more comfortable with the structure in place in Miami than St. Louis.
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The Dolphins have been in a holding pattern since hosting Fisher, but they also have continued to interview candidates. Cincinnati Bengals defensive coordinator Mike Zimmerinterviewed Tuesday, joining Green Bay Packers offensive coordinator Joe Philbin, Chicago Bears special teams coordinator Dave Toub and interim coach Todd Bowles, who coached the final three games of the season after Tony Sparano was fired.
The Rams also have continued to interview candidates while waiting to hear from Fisher. They have interviewed Arizona Cardinals defensive coordinator Ray Horton and will talk to first-year Denver Broncos defensive coordinator Dennis Allen this week. The team also received permission to interview Carolina Panthers offensive coordinator Rob Chudzinski, a person familiar with the situation told The Associated Press.