The 24-year-old has scored five goals in his last six matches, including two in the 3-0 Boxing Day win at Cardiff.
He was included in Roy Hodgson's England squad for the November friendly defeats to Chile and Germany, making a substitute appearance against the former.
And he is hopeful of gaining further international opportunities courtesy of good performances over the rest of this season, starting with the game at Everton on Sunday.
"Obviously it is an honour to play for your country and a confidence boost when you do get selected," said Rodriguez.
"It was a nice taste and you obviously want more of it so hopefully I just can just carry on improving and maybe you never know.
"All you can do is keep your head down at your club. You work as hard as you can to try and improve as a player and hopefully then it pays off.
"I have said to myself I want to improve on last year and hopefully I can carry on improving. I want to score as many as I can in each game, so hopefully I can."
After an impressive start to the season, Southampton suffered a slump in form, but the win over Cardiff reversed a run of six games without victory and Rodriguez hopes the victory in Wales can spark a resurgence.
"We felt we needed that result," he said. "We have kept the belief in what we want to do and the confidence and team spirit has always been there so it's nice to get the three points that we deserved.
"Of course you have injuries in the camp, that's always disruptive.
"But I think the lads that have come in have done extremely well. We have got a great squad that has shown by the results and hopefully we can continue to pick up points."