A decision on the appeal by the commissioner's office is expected before the season begins Sept. 3, said the source, who did not want to be identified.
The league declined to comment.
The NFL has a no-tolerance policy regarding steroid use, which means Johnson would be suspended even for his first offense.
Johnson, 26, was expected to start the Dolphins' opener against Seattle. He started four games as a rookie last year and led the team with 558 yards rushing in 164 carries with four touchdowns.
The suspension doesn't include exhibition games, but Johnson wasn't expected to play Monday night when the Dolphins faced the Green Bay Packers.
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