The 20-year-old was voted Man of the Match on his full debut for the England senior side against Brazil in midweek, keeping out the world's second-best international side in a goalless friendly at Wembley Stadium.
Gomez, brought to Liverpool from Charlton Athletic for an initial £3.5m two years ago, has nailed down a spot in the Reds' backline this season, and Klopp confirmed that he will start the youngster at right-back against Southampton on Saturday.
Asked if Gomez could become more of a regular at centre-back in the future, Klopp told reporters: "There is no doubt about that. Joe knows about his little issues but he is still a young lad.
"He has to improve in a lot of parts but of course he is ready. He is a fantastic player. He was injured in a time in his life when people are still growing and that is a medical thing. We want to have him for the next 15 years, hopefully.
"Was he a professional player at Charlton? Okay, so he is not a one-team player but we want to have him here for a long, long time. I want to use him. He is ready but he can play at full-back as well. That is very good for us."
Gomez has featured 12 times for Liverpool in all competitions this season, including nine times in the Premier League.