Away with England for the U21 Euros, Elliott says he plans to speak with management about his situation after the tournament.
"It's just a situation that me and the team have to have a conversation about because I'm coming into an age now where I'm 22, I'm going to be 23 next season," said Elliott when asked if he is considering leaving Liverpool.
"I don't really want to be wasting years on my career because it's a short career. You don't know what's going to happen.
"I need to reflect. I need to see if I'm content in doing what I'm doing and how can I improve as a player because that's the most important thing.
"I just want to improve and be the best possible version of myself. If that's to go somewhere else, then it's a decision that I'm going to have to make and I just need to see what happens.
"Nothing makes me want to leave. I love the club, I love the fans, the team. I support them as well. But most importantly, it's just about what's best for my career."