If Webb -- who was scratched from Saturday's start because of the neck problem -- continues to improve, he could throw a bullpen session on Monday and then be ready to pitch on Thursday against the Giants in Scottsdale.
The reigning National League Cy Young Award winner is slated to pitch on Opening Day against the Rockies in Colorado, and when manager Bob Melvin was asked if Webb might have to miss that start, he said, "Not if we stay on this schedule, and we anticipate that we will."
Speaking of injured starters: Randy Johnson played catch on Friday and will do so again on Saturday, with his second session of batting practice to follow.
"He played catch today here, everything went well, and whether he throws to hitters Sunday or Monday, it will be one of those two days," Melvin said.
Johnson has thrown five bullpen sessions and faced hitters in a batting practice session last Saturday.
Because of the effort Johnson expended in that session, the team decided to give him a couple of extra days rest before his next outing, but Melvin said they are still thinking that the Big Unit would be ready by mid- to late April.
Still battling: Two of the candidates for the final two spots in the rotation pitched on Friday night.
Right-hander Enrique Gonzalez was impressive in throwing four shutout innings. The only hit he allowed was a grounder that shortstop Stephen Drew made a nice play on but threw wildly to first for a base hit and an error.
"Enrique was outstanding," Melvin said. "It looked like his first few pitches of the game were probably his worst of the game. He was money the rest of the game."
Left-hander Dana Eveland was not as sharp. He allowed one run in 1 2/3 innings, but most notably, walked four batters.
"Just rushing a little bit," Melvin said. "Gets out there a little early, then the front side opens up a little bit, and now your command wavers a little bit. He knew what he was doing, sometimes it's just tough to correct it. Just mechanically out of whack today."
The outing is not expected to hurt Eveland's chances of making the team, which Melvin said were "very good" prior to the game.
"I can't commit to anything, but he's pitched well enough so far," Melvin said.
Ouch: Outfielder Carlos Quentin left the game in the third inning after his second at-bat when he injured his shoulder on a swing.
"I just wanted to get him out of there and make sure it's not much of a problem," Melvin said.
Quentin was scheduled to be the designated hitter on Saturday but instead will get the day off to receive treatment. An MRI may be taken as well.
Prepared: As trade rumors swirl around him, Jorge Julio remained unfazed.
"I'm ready for anything," said Julio, who has been traded three times in his career, including twice in a five-month span last year.
Most of the published rumors have centered around the Marlins, but a baseball source said that the D-backs were talking to as many as five or six teams.
And he knows it: Infielder Alberto Callaspo entered Friday as the team's leading hitter, with a .500 batting average (14-for-28), and figures to get plenty of playing time in a reserve role at second, short and third this year.
"To keep him productive and keep him involved, he's going to have to get some at-bats," Melvin said. "So these guys are going to get some days off, and he's going to be involved in it, too. He knows he's good. I like that. I don't think for a second that he thinks anybody out there is better than him, and that's the way we want it."
Up next: The D-backs will travel to Surprise, Ariz., on Saturday to take on the Royals. Dustin Nippert will make the start in place of tWebb. The right-hander is one of those still battling for one of the final two spots in the rotation. Jose Valverde, Brandon Lyon and Juan Cruz are scheduled to follow Nippert to the mound.
Gil Meche will start for Kansas City.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.