Ponson, 31, pitched in one game at Triple-A Scranton/Wilkes-Barre, allowing one run through four innings in a start on June 21 against Toledo. Ponson threw 78 pitches in that start and is expected to be capable of throwing 100 or so pitches in the Majors.
Though he was transferred to Double-A Trenton in a paper move, Ponson has remained with the Triple-A team and is preparing for Friday's start. Girardi said that the reports have been encouraging.
"They said he looked good," Girardi said. "He's doing side work and he'll be ready to go for us."
Ponson pitched briefly for the Yankees in 2006 and has had a turbulent career, pitching for six Major League teams. He had performed well for the Rangers after making the team out of Spring Training, going 4-1 with a 3.88 ERA, but Texas designated Ponson for assignment on June 6, prompted by off-the-field incidents.
Reports indicated that Ponson created a serious disturbance at a hotel bar in St. Petersburg during a recent Rangers road trip, and also acted furiously after being removed from a start against the Indians on June 4.
Ponson also engaged manager Ron Washington in a heated discussion after being informed that his next start would be pushed back so that Kevin Millwood could start for Texas on regular rest, after which a decision was reached to remove Ponson from the organization.
Girardi said that he was not concerned by the reports out of Texas, but would not commit to the certainty of Ponson making more than one start for the Yankees. He did note that several players had spoken positively of Ponson as a teammate in 2006, when he was 0-1 with a 10.47 ERA in five games (three starts).
"I think that anyone that comes over here, we need to make our own evaluation of the person," Girardi said. "We'll treat Sidney with respect and we expect the same thing from all of our players. We'll make our own evaluation, and it's our job to get the most out of him."
Giese, 31, made his first Major League start on Saturday in the Yankees' 6-0 loss to the Reds. He hurled six scoreless innings before being charged with three unearned runs in the seventh as a result of his own error, a wide throw to second base on what could have been a double-play ball. He has never faced the Mets, while Ponson has made three career starts against the Mets, last in 2003.
The Mets will counter with Mike Pelfrey in the first game at Yankee Stadium, and Pedro Martinez will be on the mound in the second game at Shea Stadium.