Either way, they need to make a decision before the team plane leaves for New York on Monday.
"Because of the off-day, if we did put him on the disabled list, he would only miss two starts and be able to come back on day 16. We're working through that," Pirates GM Neal Huntington said. "We want to be respectful of Gerrit, who wants the ball and wants to go compete. We also want to be respectful of our desire and need to have him make 30-plus starts this year.
"If we can knock this out in 15 days, we might be better served to knock this out in 15 days. We're not there yet. His next start is certainly in doubt, almost certainly not going to happen. So then you look at, 'How do we put him in position to be successful for the rest of the season?' Maybe missing that second start might be the best way to do that. Nothing definitive as of right now, but we'll see where the information goes."
If the Pirates keep their rotation in its current order, Cole's next turn would come Wednesday against the Mets at Citi Field because, with an off-day on Monday, left-hander Jeff Locke could pitch Tuesday's series opener.
If Cole goes on the disabled list, the Pirates likely would call up Jameson Taillon -- scheduled to pitch Tuesday for Triple-A Indianapolis -- for his second big league start.
Taillon made his big league debut against the Mets at PNC Park on Wednesday, allowing three runs over six innings. He was optioned to Triple-A on Thursday, and he must remain down in the Minors for 10 days. The only way he can be called back up is to replace a player heading to the disabled list.
Huntington said the Pirates thought Taillon was on the "front end of the readiness curve" when he made his debut, but the Bucs were impressed by the top prospect's poise against the defending National League champions.
"If we decide to go ahead and put Gerrit on the disabled list, then Jameson certainly becomes that candidate to come in," Huntington said. "In a perfect world, now he never goes back to Triple-A because that means we were wrong and he was more ready than maybe we gave him credit for."
Adam Berry has covered the Pirates for MLB.com since 2015. Follow him on Twitter at @adamdberry. This story was not subject to the approval of Major League Baseball or its clubs.