Aikman told the newspaper he's not trying to pressure Cowboys owner Jerry Jones, saying, "I know Jimmy's day will come."
The Cowboys' Ring of Honor -- which honors former players, coaches and personnel -- began with the induction of defensive tackle Bob Lilly in 1975. Aikman, Irvin and Smith are among 17 Ring of Honor inductees.
The only coach among the inductees is Tom Landry.
Johnson led the team to Super Bowl victories following the 1992 and 1993 seasons. He left the team following the 1993 season, partly because of clashes with Jones.