The Padres have 60 players remaining in big league camp.
Asuaje, who came to the Padres from the Red Sox in the Craig Kimbrel deal, went 1-for-6 with two strikeouts in four games during the first week of Cactus League play.
Asuaje, who is ranked the organization's No. 17 prospect, can play several infield positions. The 24-year-old will likely begin the regular season with Triple-A El Paso.
"He did a tremendous job here," manager Andy Green said. "His work ethic was off the charts. He was engaged in learning."
Arias, 25, appeared in one Cactus League game this spring for the Padres, allowing three earned runs and two walks against the Rockies on Saturday while recording just one out.
Arias hasn't pitched above Class A and could open the season with Class A Advanced Lake Elsinore or possibly Double-A San Antonio in the regular season.
Green said the Padres will take a look at having Arias throw from a sidearm slot as he heads to Minor League camp.
"There's some intrigue with him maybe in messing with his arm slot, see what he can do from the side," Green said. "He's incredibly natural from the side. They are going to see how that plays in Minor League camp."
• Outfielder Alex Dickerson suffered a slight tweak of his left hamstring in a defensive drill on Sunday, and Green said he will be kept from games for "a day or two."
"He felt good by his own admission," said Green, who noted that Dickerson will still be able to take batting practice on Monday.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.