"We haven't had any dialogue since the numbers were filed," D-backs general manager Kevin Towers said.
Teams and salary arbitration-eligible players submitted their respective salary figures Jan. 18. The D-backs filed at $4.7 million, while Johnson's side is seeking $6.5 million. If an agreement cannot be reached, the two sides will go before an arbitration panel, which must pick one number over the other.
Johnson, who declined to comment on the process, made $2.35 million in 2010.
Major League Baseball does not announce the specific dates of arbitration hearings, but they can take place any time between Feb. 1-21.
Johnson was signed as a free agent by the D-backs last December after he was not tendered a contract by the Braves following the 2009 season.
With Arizona last season, Johnson hit .284 with 26 homers and 71 RBIs. His best month came in April, when he won the National League's Player of the Month Award by hitting .313 with eight doubles and nine homers.
The D-backs have settled with their other arbitration-eligible players, signing shortstop Stephen Drew to a two-year deal while reaching one-year contracts with catcher Miguel Montero and left-handed pitcher Joe Saunders.
In the arbitration process, each side uses comparable players, or "comps," to try to justify their salary figure. Sometimes the comparables are more readily agreed upon by the two sides, but in other cases, there is a wide chasm.
"We're going to try and create some dialogue," Towers said. "This case may be a little tougher. It's a pretty tough case."
The D-backs have not been to a hearing with a player since losing to Damian Miller in 2001. The only other time they have been involved in a hearing was 1998, when they beat Jorge Fabregas.
In his 14 years as a GM in San Diego, Towers went to a hearing twice -- with pitcher Joey Hamilton and infielder Todd Walker -- and lost both times. It is not a process that Towers enjoys.
"If we can settle, that's great," Towers said. "But if we can't, we can't, and we'll go to a hearing."