Giambi has been sidelined since May 30, when he suffered a partially torn plantar fascia in his left foot while running out a home run at Toronto's Rogers Centre. Giambi is expected to briefly remain with Tampa, where he entered Wednesday's action 4-for-13 since beginning the rehab assignment, before joining the Triple-A club as it opens a weekend series at home.
From there, the picture becomes unclear for the Yankees, who have been utilizing Johnny Damon as a designated hitter in Giambi's absence while also promoting budding power threat Shelley Duncan, who served as the Yankees DH on Wednesday.
"Jason seems to be ready," said Damon, who said he received word from Giambi through the players' wives. "He says he's ready to go. ... We'd like to see a few home runs from him up here instead of down there."
Giambi is expected to work out at first base on his rehab assignment to give the Yankees a better idea of his mobility, but that position is even more crowded at the big league level -- Andy Phillips has performed more than capably after a late June callup, while Miguel Cairo and Wilson Betemit are likely to fill in the depth chart behind the starter.
Torre said that he didn't know if Giambi would see any innings in the field when he returned to the Major League level, but did not want to tie his hands by ruling it out.
"The last thing we want to do is worry about what's going to happen next week," Torre said.
Aug. 1 adjustments: One day after the non-waiver trade deadline, the Yankees reassembled their club, adjusting after Tuesday's deal with the Los Angeles Dodgers. New York activated right-hander Jeff Karstens from the 60-day disabled list to help fill the void left by Scott Proctor, who was dealt for Betemit.
Karstens was scheduled to make his sixth and final rehab start on Thursday for Triple-A Scranton/Wilkes-Barre, so the afternoon message to report to New York's bullpen came as a surprise.
"It doesn't really matter, you know," Karstens said. "Pitching is pitching. You've just got to go out there and take the same thing. Granted, it's a little bit nicer when you start because you know when you're going to throw, but regardless, I just want to come back and help."
Karstens will be appearing in the Majors for the first time since April 28, when he suffered a fractured right fibula after being struck with a first-inning line drive off the bat of Boston's Julio Lugo. In his five rehab starts, over which he fared 3-0 with a 1.07 ERA, Karstens said he has become more mindful of balls hit up the middle.
"To be honest, it's kind of been like a magnet," Karstens said. "In every rehab start, there has been a line drive up the middle. Even during the game, balls seem to find me somehow. You've just got to laugh it off and take it like it comes."
Betemit arrived in New York less than an hour before game time and assumed the roster spot held by rookie Chris Basak, who was optioned to Scranton/Wilkes-Barre.
Papers in order: The Yankees aren't yet prepared to call up 21-year-old prospect Joba Chamberlain for relief help, but the wheels may be in motion. A sign was posted in the Yankees clubhouse Wednesday reminding players to secure their passports for the club's upcoming flight to Toronto on Aug. 6.
By coincidence, Chamberlain -- a first-round selection of the Yankees in last year's First-Year Player Draft -- was summoned to New York on Wednesday afternoon to make sure his paperwork would be in order for an international flight. Chamberlain was also reassigned to Double-A Trenton, where he will report for a road series against the Mets' Binghamton affiliate.
Phantom curtain call: Torre offered a heartfelt apology to Duncan after sending him out for a curtain call in the eighth inning of Tuesday's 16-3 slugfest, when Duncan slammed the final of a record-tying eight New York home runs. After Duncan achieved cult hero status by slugging three home runs last weekend against the Tampa Bay Devil Rays, Torre said he simply assumed the roaring ovations were for Duncan, the excitable young rookie whom the manager called "sort of like our mascot."
In fact, they were for Alex Rodriguez, who was coming to bat for his final at-bat in a fruitless effort to hit home run No. 500. Torre said that Duncan probably didn't believe the apology, thinking that they were just playing a joke on the rookie.
"I just do what I'm told," Duncan said.
Bombers bits: Doug Mientkiewicz is expected to be cleared for hitting on Thursday, pending the results of a precautionary bone scan. ... The Yankees compiled a Major League-best .679 winning percentage in July, faring 19-9. ... New York's 208 runs in July marked just the second time in the expansion era that the Yankees exceeded 200 runs in a calendar month, according to the Elias Sports Bureau. The 1998 Yankees scored 222 runs in August.
Coming up: The Yankees and White Sox play the third and final game of their mid-week series on Thursday at Yankee Stadium, with right-hander Roger Clemens (3-5, 3.92 ERA) heading to the hill for New York. Chicago counters with right-hander Jon Garland (8-7, 4.12 ERA), with first pitch set for 1:05 p.m. ET.