Upton, signed to the biggest contract in franchise history at five years, $75.25 million, has a .146 batting average, 109 points below his seven-year career mark with Tampa Bay.
Gonzalez indicated that Upton has enough service time in the majors to refuse an assignment if he disagrees with the move.
"In my own mind, you think about those things, but really I haven't gotten to that point," Gonzalez said. "I think there's some logistics -- contractual things and that sort of stuff -- that they might not be able to do it that easy."
Upton was not available for comment before Atlanta hosted the Washington Nationals.
Gonzalez has spoken with Upton about his absence from the lineup, but not about an assignment in the minors.
"He understands to a certain point," Gonzalez said. "Like good players do, they want to play. We've had conversations and he's making the adjustments and we'll see."
Upton is hitless in the Braves' past seven games. He was out of the lineup Friday for the second straight night.
"They work," Gonzalez said. "You've got to really tip your hat and really root for them because they really work it, show up and bust their butts."
Upton, Heyward and Uggla were out of the lineup in Thursday's 11-3 win over Toronto. Heyward pinch hit in the seventh inning and reached on catcher's interference before playing the rest of the game.
Against Washington, Heyward was batting leadoff for the second time in his four-year career and first time since going 1-for-4 in a 3-1 win at Seattle on June 27, 2011.
Heyward, who started in center field for the second time this season, is hitting .195 in 12 games since returning May 17 from an appendectomy.
Heyward began the night 7-for-14 in his career against Nationals ace Stephen Strasburg. He wasn't surprised that Gonzalez moved him to the top spot in the batting order.
"Anything can happen throughout the year," Heyward said. "You can never count one thing out. You can never guarantee one thing. It's a 162-game season, so anything is possible. Whatever is best for the team on any given night needs to be done."
Upton's lack of playing time has coincided with the consistent power numbers being produced by rookie Evan Gattis, who has been getting starts in left field following catcher Brian McCann's return May 6 from shoulder surgery.
Gattis leads all rookies with 12 homers, 23 extra-base hits and 32 RBIs despite getting just 137 at-bats.
"Every time you run him in there, he does something, you know?" Gonzalez said.
Regarding Upton's immediate future and whether the Braves might ask him to accept an assignment in the minors, Gonzalez said the Braves have no timetable.
"It's a hard decision," Gonzalez said. "It's a decision that you take very, very seriously. You talk collectively with your coaches about it, and it's something always falls on my shoulders, right? That's fine. I'm comfortable with that. But you've got to think about 25 (players), six staff members, four clubhouse guys, the front office and the fans."