Rodriguez refused to address the topic on three occasions Tuesday, once saying "no" when asked if he had any comment.
Yankees co-chairman Hank Steinbrenner also criticized the team's lack of hitting before an 18-7 win over the Texas Rangers on Wednesday night, suggesting "a little less outside distractions and a little more concentrating" might help the team at the plate.
The Daily News reported Wednesday night, citing an anonymous source, that Rodriguez and wife, Cynthia, have separated after having "problems" for about three months.
The couple was married in November 2002 and has two children, Natasha Alexander and Ella Alexander, who was born April 21.
Rodriguez went 2-for-3 Wednesday night with his 17th homer of the season and also scored four times. It also was Rodriguez's 535th homer, moving him past Jimmie Foxx for 14th on the career list.
Information from The Associated Press was used in this report.