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It's said that the Reds will demand a fee in excess of £40m while including a buy-back clause, or above £50m without one.
Tottenham, Brentford and RB Leipzig were both linked while Elliott impressed for the Young Lions in Slovakia.
"I think it's a situation that me and the team on my behalf have to have a conversation about," the former Fulham wonderkid said ahead of the Euros.
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"I'm coming into an age now where I'm 22 - I'm gonna be 23 next season - and I don't really want to be wasting years in my career because it's a short career, you don't know what's gonna happen.
"Injuries and things could shorten it.
So I think it's a situation that, as I've said before, 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.
"That's the most important thing, that's the main thing really, I just want to improve and be the best possible version of myself and the best player I can be.
And if that's to go somewhere else then it's a decision that I'm going to have to make, I just need to see what happens."
Which club should sign Harvey Elliott?
"I think first of all it's very important that players who are here with us would like to stay, that’s a bit compliment to everyone working here," the Liverpool manager explained.
"Harvey is one of the players who hasn't had as much playing time as he maybe deserves, but like some others he’s in competition with so many good players that mainly I've chosen.
There was no need for me to start with different players, but I think if you look at the amount of minutes that he had in the last one or two months and the time before, you can see it goes up already.
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