On Sunday, he threw 25 pitches at about three-quarters strength and said everything felt normal. He is scheduled for another bullpen session Wednesday after throwing only fastballs and a few changeups in his first session.
"I will start mixing in curveballs and it will be about 35 pitches or so," he said.
Walker, 21, has been rehabbing or resting from pretty much the outset of Spring Training after inflammation was discovered in his right throwing shoulder in late February.
"I'm concerned about the guys I have," manager Lloyd McClendon said, "not about the guys I don't have. So until they're part of this 25-man roster I'm not concerning myself with it.
"When they can throw out on that mound and throw 60 feet, 6 inches, I'm concerned about them."
Meanwhile, Paxton threw 40 pitches off a mound -- fastballs, curveballs and changeups -- with about 80 to 85 percent intensity. The plan for him is to throw a 55-pitch bullpen on Wednesday and then go from there.
Paxton hasn't appeared in a game since injuring his left lat muscle in the Mariners home opener April 8. In two starts this season, the 25-year-old lefty is 2-0 with a 2.25 ERA in 12 innings.
"It kinda sucks," he said about sitting out. "It does feel like a while, but it's nice with the team in town and being able to watch the games and being a part of that."
Adam Lewis is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.