Druckenmiller, 27, hasn't thrown a pass in a regular-season game since 1997, his rookie season with San Francisco. He was taken with the 26th pick in the draft that year by the 49ers, then traded in September 1999 to Miami for a seventh-round pick in this year's draft.
Fiedler has been sidelined by a hip injury but is expected to return to practice Saturday.
"At this point, I don't believe that Jim could challenge for the starting job," coach Dave Wannstedt said in a statement. "So I wanted to make this move to give Jim a chance to explore other options in the league."
Druckenmiller's agent, Gary Wichard, didn't immediately return a call seeking comment. Druckenmiller said last week he would welcome going to another team if it improved his chances of playing.
His only action this preseason came in Miami's first game Aug. 5, when he completed 13 of 21 passes for 141 yards against the Pittsburgh Steelers.
Druckenmiller played in four games as a rookie, starting once when Steve Young was hurt. At 6-5 and 230 pounds, he's impressive physically and had the strongest arm in the Dolphins' training camp, but he struggled reading defenses and reacting to the pass rush.
When asked last week whether he received a fair chance with the Dolphins, Druckenmiller chuckled and said, "That's a good question."
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