"He's due to DH on Sunday [at Triple-A]. If he gets through the weekend fine, and he responds to the DH fine and flying from Scranton to join us in Texas, all that is fine and he's like, 'I'm ready to go,' [then] he's in there," Cashman said.
Cashman left some wiggle room in case Rodriguez is fatigued, saying that the Yankees would be willing to push Rodriguez's 2013 debut to Tuesday, if necessary.
"Ultimately the hope is that he's ready for us on Monday," Cashman said.
Brent Lillibridge became the most recent addition to the Yankees' third-base carousel on Friday. Kevin Youkilis, David Adams, Jayson Nix, Chris Nelson and Luis Cruz entered play Friday having combined for four homers and 28 RBIs, the lowest hot-corner production in the American League.
"I think [Rodriguez] will be better than the production we've gotten from third so far this year, all due respect to everyone else," Cashman said.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.