The newspaper, citing unidentified "individuals familiar with the episode," reported Thursday night that Hamilton was at a Dallas area bar Monday.
In a statement to the newspaper, the Rangers said they were "aware of a situation, but we don't have further comment at this time."
Hamilton, 31, was suspended for more than three years for drug and alcohol use while in the Tampa Bay organization. He missed the entire 2004-05 seasons. He won the AL MVP in 2010.
This was Hamilton's second alcohol-related relapse in three years. In January, 2009, he drank to excess in a bar in Tempe, Ariz.
