The two teams have "been in contact" to discuss a potential deal for the American League's All-Star Game starter behind the plate.
Ramos entered Thursday hitting .291 with a .340 on-base percentage and 14 home runs in 75 games.
The 30-year-old is in the last season of a two-year deal with the Rays after spending the bulk of his career with the Washington Nationals. Interestingly, the Nats are also interested in trading for the catcher, according to Jon Heyman of Fancred.
With Tampa Bay currently 9.5 games out of an American League wild-card spot, it could make sense to deal the pending free agent to the highest bidder.
Meanwhile, the Astros remain a top World Series contender with the second-best record in the majors at 62-33, trailing only the Boston Red Sox by 3.5 games. Unfortunately, they have question marks at catcher after Brian McCann suffered a knee injury.
According to Ken Rosenthal of The Athletic, he is expected to miss four to six weeks from the start of July.
Although Max Stassi has filled in well, adding a two-time All-Star like Ramos could be a game-changing move to potentially bring home another championship.