Girardi said that right-handers Luis Severino and Bryan Mitchell are not options; Severino pitched on Friday for Triple-A Scranton/Wilkes-Barre and Mitchell is starting on Saturday, effectively ruling out both pitchers.
"A lot of it depends on what happens over the next few days and who we have available to do it," Girardi said. "It could be a situation where you throw one guy three innings, another guy four innings, that sort of situation."
It is possible, of course, that Tuesday's starter could come from outside the organization. The Yankees are known to have engaged with the pitching marketplace in advance of the July 31 non-waiver Trade Deadline, though no deal appears imminent.
Even though Girardi noted that inserting another starter offers rest to all of the Yanks' starters, the move appears to be focused on Tanaka, who will start on Wednesday at Texas and has not pitched on four days' rest since he sustained a right forearm strain on April 23 against the Tigers.
Girardi said it is possible that the Yankees will continue to pitch Tanaka on an extra day of rest for the remainder of the season; thanks to an off-day on Aug. 3, he would be lined up to start on Aug. 4 with that extra rest, and the team wouldn't need to use a sixth starter.
"He's pitched pretty well on that extra day's rest and it's just, we feel that he's probably comfortable doing that," Girardi said. "We want to protect him and we want to protect Michael [Pineda] and protect CC [Sabathia]. You want to protect everyone in this situation, so we're going to do it."
Ivan Nova is starting the series opener at Texas on Monday. Pineda will follow Tanaka and pitch on Thursday.
"We feel like it's the best for all of our starters," Girardi said. "I'll reiterate, the only one that you really feel comfortable going 200 innings is probably [Nathan] Eovaldi. CC, I feel comfortable, but with what he's had to deal with, it's a little bit of a stretch."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch, on Facebook and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.