Rodriguez's alleged participation was first reported by The Associated Press in early July. On Wednesday, ESPN.com cited an anonymous source who said Rodriguez could face suspension if it is confirmed that he participated in the games. On Thursday, the site credited an anonymous source who said a conversation between Rodriguez and MLB could take place "in the next couple of weeks."
Star Magazine reported last month that several people saw A-Rod playing in games hosted at Hollywood hotels and residences. According to ESPN.com, Rodriguez's publicist, Richard Rubenstein, issued a statement that said the Star story "contains numerous factual inaccuracies."
Rodriguez, rehabbing in Tampa, Fla., from knee surgery last month, declined to comment Thursday.
Yankees general manager Brian Cashman told ESPN.com on Wednesday, "I don't know anything about it." Manager Joe Girardi declined comment, saying: "Let baseball handle those things."
Rodriguez was warned about illegal gambling by the Yankees and Commissioner Bud Selig in 2005.
"We take this very seriously and have been investigating this matter since the initial allegation. As part of the investigation, the Commissioner's Office will interview Mr. Rodriguez," MLB said in a statement Wednesday.