The New York Times reported the meeting will take place Sunday.
Despite that, Rodriguez traveled with the Yankees to Ed Smith Stadium in Sarasota, Fla., for an exhibition contest Sunday against the Cincinnati Reds.
Rodriguez, who was in the starting lineup, didn't talk to reporters after taking batting practice before the game.
Rodriguez admitted to using performance-enhancing drugs from 2001 to 2003 while he was with the Texas Rangers. MLB wants to speak with Rodriguez regarding security issues and his past involvement with performance-enhancing drugs.
Yankees manager Joe Girardi said Rodriguez would like to push back the date of the meeting. Sunday was to be Rodriguez's final game with the Yankees before he reports to the Dominican Republic squad for the World Baseball Classic.
"I think that Alex is hoping that it's possibly not tomorrow, a later date," Girardi told MLB.com. "He talked to me a little bit today about it, that he's hoping it's not tomorrow."
Up for possible discussion at the meeting are Rodriguez's relationships with Angel Presinal, a trainer banned from MLB clubhouses, and with Rodriguez's cousin, Yuri Sucart. A-Rod said Sucart repeatedly injected him with a banned substance that was brought into the United States from the Dominican Republic.
Information from The Associated Press contributed to this report.