Rodriguez was a surprise inclusion in Hodgson's squad for the upcoming friendlies against Chile and Germany.
The 24-year-old has been in decent form for Southampton this season, scoring four goals in 14 games and with just three friendlies to go until the announcement of England's provisional World Cup squad, Rodriguez is keen to show the manager what he can do.
"I need to try and impress, work as hard as I can and see how this week goes and try to make an impression," the striker told FA TV.
"Every player wants to work towards (an England call-up)," he added. "To represent your country is the best thing to do in your career.
"I just wanted to work hard, get my head down and try to improve and then my form would hopefully see me sneak in."
Rodriguez may have a Spanish surname thanks to his father Kiko, but his Lancashire accent is so broad that he would not sound out of place on Coronation Street.
It is clear that Rodriguez regards himself as very much an Englishman.
The Burnley-born striker counts Steven Gerrard and Frank Lampard as two of his childhood heroes, and he admits it is a strange experience training alongside the England duo, who have 209 caps between them.
He continued: "I've always watched Gerrard and Lampard, they are unbelievable, so to meet them is unreal and a great feeling.
"I remember watching the World Cup games, it's a bit surreal watching the games at home, and then being here is great."
Rodriguez's only previous experience of international football came two years ago in his only appearance for the Under-21s against Italy.
Rodriguez admits he and fellow uncapped team-mate Adam Lallana felt pangs of anxiety after being told they were in the squad.
The step up from domestic to international level has been helped by another Saint in Rickie Lambert, who drove the pair up to Watford where the squad met on Tuesday.
"It was really exciting driving up, we were anxious to meet everyone," Rodriguez said.
"We were asking Rickie about the plans for the week and how he found it. It's been a good experience so far.
"It's very good to meet all the players and the staff and see how things run.
"The pace and the quality (in training) is unreal, it's something I've learned so far.
"It's great to be on the training pitch with these players who are in the squad.
"I couldn't believe it when I got the call. I told my dad and some friends and family. It was unbelievable, I couldn't stop smiling, it was a great feeling and to be here now is really good."