Recovering from elbow ligament-replacement surgery in June last year, Beachy gave up three runs - two earned - on three hits and four walks in three innings Thursday for Triple-A Gwinnett at Rochester. He is 2-1 with a 3.27 ERA in five minor-league rehab starts.
Beachy, who was with the Braves on Friday, is scheduled to throw on the side on Saturday.
"If everything goes well we expect him to pitch one of the games on Tuesday," Gonzalez said.
New York's probable starters are Matt Harvey and Zack Wheeler, who will be making his major league debut.
The Braves need an extra starting pitcher for the doubleheader but then must make a decision on how to make room for Beachy in the rotation.
"Those things have a tendency to work out," Gonzalez said.
The current rotation includes Tim Hudson, Mike Minor, Kris Medlen, Paul Maholm and Julio Teheran. The bullpen has lost left-handers Jonny Venters and Eric O'Flaherty to season-ending elbow injuries.
Beachy was perhaps Atlanta's top starter when his 2012 season ended, leading the NL with a 2.00 ERA. He was 7-3 with a 3.68 ERA in 2011.
Braves spokesman Brad Hainje said Beachy, who declined interview requests, was to be examined by a team doctor during the Braves-Giants game on Friday night.
Brandon Beachy
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