Rodriguez is scheduled to play another Minor League rehabilitation game on Saturday for Double-A Trenton, which will be his 15th game in the Minors this year overall.
After that, the Yankees are proceeding as though Rodriguez could join them in Chicago on Monday. It has been widely reported that Major League Baseball is planning to hand Rodriguez a substantial suspension, but nothing has yet been announced.
"I heard it was going to be this week; I heard it was going to be on Thursday," Girardi said. "Deadlines aren't deadlines until someone actually pulls the plug here and says something. They say it's going to be Monday. I don't know. Our goal is to have him here on Monday."
Girardi had little reaction to Rodriguez's postgame comments on Friday, in which he told reporters, "There's more than one party that benefits from me not ever stepping back on the field. That's not my teammates and it's not the Yankee fans."
"My goal is to get him back here as a player for us," Girardi said. "That's my goal. I manage the players in the clubhouse. That's my job. My goal is to get him back. I hope we have him back on Monday."
Girardi said there was no chance Rodriguez, who homered for Trenton on Friday, would be in San Diego for Sunday's 4:10 p.m. ET game against the Padres.
"I don't think we can get a fighter jet to get him here in an hour or two. I don't think that's going to happen," Girardi 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.