It's the second round of contract talks, after a previous deal was rejected by pilots in a vote last year.
The pilot contract negotiations fall under the Railway Labor Act, which governs airline labor relations. The pilots union would have to clear a number of hurdles to be able to strike.
"Our negotiators are working diligently to obtain the contract that we deserve," Malone wrote in a letter to pilots.
The union's announcement of the opening of an Atlanta "strike center" comes after its parent organization, Air Line Pilots Association International, recently granted its request for $5 million to help fund a strike and "strike-related efforts."
In letter to pilots, Malone wrote last month that the pace of negotiations had accelerated, and earlier this month wrote that the union's negotiating committee "reported good progress at the table," having completed several sections of the contract.
But he also wrote: "I am planning for all contingencies: for a deal or no deal."
The pilots union in its opening proposal sought a nearly 40 percent compounded pay raise over a three year period. On Tuesday, Malone wrote that reactions from pilots to the company's pay proposal "indicate overwhelming disappointment with this offer," while adding that he sees it as a starting point in talks on pay.