Published reports indicated the Giants have interest in his services after they lost catcher Buster Posey, who is on the disabled list for a lengthy period because of a broken leg and sprained ankle.
However, Rodriguez said he made it clear to general manager Mike Rizzo that he wants to stay with the Nationals.
"Nobody told me anything," Rodriguez said. "But I can tell you one thing: I feel good where I am. I think this is a great team to be on -- nice group of guys. I told Rizzo that. I'm not thinking about it.
"I play for the Washington Nationals right now. I'm focusing on winning ballgames and be a good teammate. Those rumors, I've heard it a lot in my 21 years. I'll concentrate on playing my game. This is a great group of guys, great team, great organization. The fans are great and I'm happy where I am."
Rodriguez is splitting time with Wilson Ramos behind the plate. However, Ramos is expected to be the everyday catcher after the All-Star break.
In 23 games, Rodrigurez is hitting .211 with two home runs and 14 RBIs.