Cole went 7-3 with a 2.84 ERA over 12 starts in last year's abbreviated season, his first in pinstripes after signing a $324 million, nine-year contract as a free agent. Boone said Cole's appearance in the opener is "safe to say.''
"I thought his stuff was pretty good,'' Boone said after Cole threw 26 pitches during a five-batter outing. "Command is not where it's, obviously, going to be for Gerrit Cole. But just another good step for him. He used all of his pitches and I think did exactly what he needed to do today to take that next step in his progression to get ready for the season.''
Right-hander Luis Severino, coming back from Tommy John surgery last February, expects to advance to throwing other pitches in addition to fastballs next week. He remains on target to return in June or July.
"Mentally, physically, I feel pretty good,'' Severino said.
Severino threw at 90 feet on level ground and will move to 120 feet on Tuesday.
Kluber has been limited to one inning since May 2019 by right forearm and shoulder injuries. The two-time Cy Young Award winner signed an $11 million, one-year contract.
Taillon was acquired by the Yankees from Pittsburgh on Jan. 24 for four prospects. He has not pitched since May 2019 while rehabilitating from his second Tommy John surgery.
With several off days early in the season, Boone figures he will be a little creative with the rotation during the opening two weeks.
"Just being mindful of guys like Jameson and Kluber coming off a season where they didn't pitch,'' Boone said. "Just wanting to build guys up and feeling like we have a number of guys that are ready to be contributors. It will allow us to be strategic with how we line them up.''
Left-hander Jordan Montgomery also is expected to be in the rotation.
A competition for fifth starter is unfolding among Deivi Garcia, Domingo German, Michael King and Jhoulys Chacin. Clarke Schmidt had been in the mix but has been shut down for three to four weeks due to a strained common extensor tendon near his elbow in his right arm.
3B Gio Urshela (elbow surgery) could be ready to play in Sunday's spring training opener against Toronto.
The first full-squad workout is Tuesday.