According to Melvin, Casilla has been maintaining a throwing program at the team's academy in his home country, while also playing the role of mentor to the young players there.
"If we get into games and he's not here yet I might get a little antsy," said Melvin, whose club opens Cactus League play Saturday against the Cubs. "At this point, I'm not. I'm not worried about him. It's a long spring."
• Spring Training: Info | Tickets | Schedule | Gear
The spring season was extended this year to accommodate the World Baseball Classic, which Casilla has committed to play for the Dominican Republic. Melvin said he would like to see Casilla throw off the mound a few times before getting him in exhibition games.
Casilla, 36, comes back to the A's after seven seasons with the Giants. He posted a 3.57 ERA with 31 saves last season, after compiling a 2.79 ERA and a career-high 38 saves in 2015.
• Oakland's 2016 first-round Draft pick, left-hander A.J. Puk, "threw the ball really well" in his first live batting practice, Melvin noted.
"He had quite a crowd around his cage, too, which, when you're a young kid, you tend to notice that," he said, "and I thought he responded to that pretty well. He's been impressive here."
Jane Lee has covered the A's for MLB.com since 2010. Follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.