The 44-year-old right-hander had returned home to Texas following his 102-pitch effort on Wednesday for Double-A Trenton of the Eastern League.
"It's hard to be ready, especially after just two," Cashman said. "We want him when he's ready, no sooner than that and no later than that. His preparation to get back and try to help this team takes its next step into Scranton, and we'll see what we see after Monday."
Clemens will be supervised every step of the way by Yankees executives Billy Connors and Gene Michael, who will accompany Clemens to PNC Field in Moosic, Pa., for the start.
The timing of the start for Scranton/Wilkes-Barre keeps alive the possibility that Clemens could make his first Major League appearance at Fenway Park, his old stomping grounds and an environment that would surely provide a charged atmosphere.
Following the start for Scranton/Wilkes-Barre, the seven-time Cy Young Award winner would have his fifth day align for Saturday against the Red Sox, a start that is presently lined up for Mike Mussina.
"We'll just take it one start at a time, and we'll evaluate him after that," Cashman said. "We want him when he's ready, and it's our job obviously to determine that. I do believe he's going in the right direction."
Manager Joe Torre did not want to shy away from the idea of having Clemens pitch at Boston, but said that it was not necessary for Clemens to make his re-entry in such a dramatic fashion.
"Fenway, as they used to say in football, is piling on," Torre said. "I don't think we necessarily need Fenway for it to be exciting."
Because the Yankees have their top three starters -- Chien-Ming Wang, Mussina and Andy Pettitte -- set to pitch against the American League East-leading Red Sox, Torre said it remains possible that Clemens could miss the Boston series entirely and make his debut against the White Sox in Chicago.
The Yankees open a four-game series at U.S. Cellular Field on June 4.
"If Roger's ready, we certainly have to figure out a way where the inconvenience would be minimal," Torre said. "That involves everybody. He's going to fit into a slot to be one of the starters, and we'll just have to see what is best for everybody."
Cashman said that Clemens would be receptive to whatever the Yankees deem necessary. If they needed him immediately, Cashman said, he would report to the Major Leagues. Since that is not the case, the Yankees can afford to allow Clemens at least one more opportunity to sharpen his repertoire in preparation.
"I consider him like a raging bull. He's a guy who understands the process," Cashman said. "He's included in the process. He wants to get up here when he's ready to help."
Clemens threw 102 pitches -- 64 for strikes -- over 5 1/3 innings for Double-A Trenton on Wednesday. He allowed three runs and six hits over 5 1/3 innings, walking four and fanning five.
"The thing that impressed me is how many pitches he threw," Torre said.
In his first start, for the Class A Tampa Yankees, he gave one run on one hit over four innings.
Clemens signed a one-year, prorated, $28 million contract on May 6, returning to the Yankees, for whom he pitched from 1999-2003. Clemens began his workouts at the University of Kentucky campus before beginning his Minor League tour of duty at Legends Field in Tampa.