Yankees left-hander Andy Pettitte (fractured left fibula) is expected to face hitters on Wednesday, Girardi said, and right-hander Ivan Nova (right shoulder inflammation) is expected to do the same on Tuesday or Wednesday.
Yankees general manager Brian Cashman has joined the club for the trip to St. Petersburg.
Girardi again defended catcher Russell Martin's offense before Monday's game. Martin entered play batting .195 with 14 home runs and 36 RBIs in 109 games.
"I think he's hit the ball a lot harder than what the numbers indicate," Girardi said. "I think he's fallen victim to a lot of bad luck. I don't know if people who see him every day agree with me, but every day we say, 'There's another lineout for Russell.' It's been unbelievable."
The Yankees have released outfielder Kosuke Fukudome, who signed with New York on July 13 and hit .264 with two home runs, 16 RBIs and a .429 on-base percentage in 43 games with Triple-A Scranton/Wilkes-Barre.
On this date in 1995, Tony Fernandez became the 10th Yankees player to hit for the cycle, doing so in a 10-9 loss to the Athletics. Melky Cabrera became the 11th and most recent to do so on Aug. 2, 2009, against the White Sox in Chicago.