On the mend from shoulder inflammation, Cook is scheduled to throw in his first bullpen session of the spring on Thursday. He'll need a handful of those under his belt before facing hitters. This means he's likely not targeted for an exhibition game for at least another two weeks, with only two more weeks remaining thereafter on the preseason schedule.
Cook appeared in nine Spring Training games last year, and though Melvin wouldn't put a number on how many he'd like to get the reliever this time, ideally it's five or six -- including back-to-back days.
"It depends how he does each and every time," said Melvin. "Whether or not we need a back-to-back, I'm not sure yet, but it'll be down to the wire probably."
The A's have more than enough depth to withstand Cook's potential absence from the Opening Day roster, but that doesn't alter their desire to have him on board right away.
"We haven't rushed it to this point," Melvin said. "We've been really careful with him. He's been feeling great for a while now. But, as far as our programs go, he's going through the regular process. So certainly the depth is a consideration, but we'd like to have him for Opening Day."
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.