Rodriguez signed for Saints from Burnley in a club record deal.
"In terms of England, I have been capped with the Under-21s. It is always a great experience to represent your country," he told the Daily Star.
"Of course, I would love to play for the senior side but at the moment I am just thinking about doing my best for Southampton and concentrating on them.
"I never think about the price tag. It does not add any extra pressure, I just want to do as well as I can for the team."