"As I'm told, I think there will be one Saturday," said Cook, "and then we'll go from there. Hopefully all goes well and then I just come back.
"It's obviously not up to me. They're going to make the best decision for the team and for my health."
Cook, sidelined since May 7 with a right forearm strain after already missing the first week of the season with right shoulder tendinitis, said on Thursday that he feels "10 times better than when I came back from the shoulder thing.
"Just in terms of sharpness and pitchability," the righty said. "Obviously I felt healthy, but I don't know that my pitchability was as good as it feels now."
Cook threw about 40 pitches on Thursday, with pitching coach Curt Young standing in against him.
Jane Lee is a reporter for MLB.com. Aaron Leibowitz is an associate reporter for MLB.com.