Bochy did not rule out the possibility that Posey, with continued progress, could play Sunday, although it would be at first base.
Posey went though the concussion protocol Saturday.
"He worked out. He did his cardio. He's going to take some swings," Bochy said. "I think they are going to run him outside. Then he'll go through another concussion test and we'll know where we are at.
"We are really optimistic as to how he feels right now. It's really encouraging for him."
Right-handed relievers Pierce Johnson and Derek Law were recalled from Triple-A on Saturday when Friday's starter Chris Stratton and Kelby Tomlinson were optioned to Sacramento.
Posey left Friday after feeling lightheaded at first base following a single to right field. Nick Hundley pinch-ran and stayed in the game at first base. Hundley started Saturday and is the only available catcher on the roster.
Bochy said infielder Chase d'Arnaud would be the front-runner for emergency catching duty after talking to him earlier Saturday. d'Arnaud's brother, Travis, is a catcher in the Mets' organization. Sacramento catcher Ronnie Freeman was flown to Phoenix just in case a move had been necessary for Posey.
Stocking the 'pen Johnson and Law added fresh arms to a bullpen that was used for eight innings in the first two games of D-backs' series against the Giants. After pitching 4 1/3 innings in the two games, left-hander Ty Blach is likely out for a day or two.
"It was a situation where we needed help today," Bochy said.
The Giants have a day off Wednesday, when Stratton's next start would have fallen, but they have options. Blach could make a spot start Thursday to give the rest of the starters an extra day, or the Giants could remain in rotation after the off-day, as all would be on normal four days' rest.
"Just exciting being able to meet him," Duggar said. "Extremely honored, for one, to have a comparison to Steve Finley. I used to watch him growing up. That was really cool."
Finley was named the center fielder on Arizona's 20th anniversary team, and he was in town this weekend as part of the celebration. Bochy wanted to make sure they met.
"I knew he played here, but I didn't know he was going to actually be here," Duggar said.
"When I first saw him, I said 'Aw, this is going to be cool.' Definitely a fun moment. Being able to talk a little bit. Learning offensively. Taking what the pitcher gives you. Little things like that, it was a lot of fun to be able to chat with him for a little bit behind the turtle [batting cage]."
Duggar, 6-foot-2 and 189, hit his homer in his 20th Major League game, and like Finley also has a speed component to his game. Duggar has two stolen bases this season and had 51 in his Minor League career since being a sixth-round choice out of Clemson in the 2015 draft.
Finley, 6-foot-2 and 175, had 304 homers and 320 stolen bases in a 19-year Major League career. He was with Bochy in San Diego from 1995-98 before signing with Arizona, and was a member of their 2001 World Series winner.
"Steve [Finley] was telling him when he was young he was a line-drive hitter and tried to use the whole field, and the power came a little bit later," Bochy said. "I had some good years with him."
On the defensive play of the game, Duggar set up a couple of steps into left field, giving him even more ground to cover before taking extra bases away from David Peralta with a lunging, snow-cone catch.
"It was high enough, so I just put my head down and started running," Duggar said. "It was one of those balls kind of in no-man's land. You don't know how far 'Cutch' is from it. I had a beat on it, but at the same time you don't know if you are going to lay out or not.
"I kind of felt Cutch's presence at the last second and tried to avoid him and just stick my glove out and try to hold onto it. I felt it in my glove, but I felt it starting to come out so I just tried to squeeze as hard as I could and fortunately hung onto it."
Jack Magruder is a writer for MLB.com based in Phoenix.