SAN FRANCISCO -- Brian Wilson threw softly off flat ground Sunday morning, a light day of work in his rehab from an inflamed right elbow, and the Giants have not yet begun to discuss the possibility of shutting down the closer for the rest of the season.

Giants manager Bruce Bochy said Wilson will throw a light bullpen session off the mound Monday after he played catch for six or seven minutes Sunday. While Bochy said the Giants are still hoping to get Wilson back, he admitted the bearded closer would likely not return if the club continues to fall further out of the playoff race.

"We haven't talked about that. Could it be a conversation? Sure. We'll see where we're at," Bochy said. "But we're still fighting to get back in this, and hopefully we do and find a way to run off a nice winning streak while we get him healthy."

Wilson has not pitched in a game since Aug. 15, when he allowed three runs on three hits and two walks in two-thirds of an inning. Entering Sunday's game, the Giants were six games behind the D-backs in the National League West with 23 games to play. With Bochy employing a closer-by-committee approach, Santiago Casilla and the rest of the Giants relievers have performed well in his absence.

Worth noting

• Right-hander Sergio Romo was not with the Giants for their series finale against the D-backs, as he flew out to Arizona on Sunday morning to join his wife, Chelsea, for the birth of their son, Rex Ryder Romo. Rex (7 pounds, 5 ounces) was born at 5:47 a.m.

• The Giants recalled catcher Hector Sanchez from Class A Advanced San Jose on Sunday, giving them a third backstop and 31 active players. Sanchez has been on the big league roster twice this season, recording his first Major League hit in his last callup, but has yet to start a game.

• Outfielder Pat Burrell was only available to pinch-hit Sunday after leaving Saturday's game in the third inning with soreness in his right foot. Burrell chose to play on his injured foot rather than undergo potentially career-ending surgery, and it will likely present a problem for the rest of the season.

"That was my concern with him on back-to-back days, to be honest," Giants manager Bruce Bochy said. "It's going to be a day-to-day thing with Pat. He'll go as he can tolerate. We'll see how he's doing tomorrow."

• Bochy clarified Sunday that he did not invite Barry Bonds into the Giants' clubhouse Saturday afternoon, when Bonds held court with several Giants players to discuss hitting and his approach to the game. Bonds was at AT&T Park to film a public service announcement as part of Strike Out Violence Night, and Bochy said the home run king drops by the clubhouse from time to time.

"He's a great hitter," Bochy said. "You never stop trying to get better or learning. He's a good one to talk to."

• Rehabbing left-handers Jonathan Sanchez and Barry Zito played catch on flat ground before Sunday's game. Both pitchers are on the disabled list and threw off the mound Saturday afternoon.