Virgil van Dijk has admitted that signing a new defender will "accelerate" Liverpool's improvement, with the Reds having held talks with Crystal Palace over a move for England international Marc Guehi.
Liverpool earned a dramatic 4-2 win over Bournemouth in their Premier League opener on Friday thanks to two late strikes from Federico Chiesa and Mohamed Salah. However, their defensive performance came in for criticism and they also conceded twice to Crystal Palace in the Community Shield.
Liverpool have signed a new defender, bringing in teenage prospect Giovanni Leoni from Parma, but BBC Sport are reporting that the club have also held initial talks with Palace about a move for Guehi.
Palace are said to want around £40million for the centre-back, who is out of contract next summer, and Van Dijk was asked about the prospect of Liverpool signing a new defender after their win over Bournemouth.
"You can say you have to accelerate it (improvement) but that is down to the market," Van Dijk said. "We have to focus on what's here and now. I think it (defensively) was much more improved than the last game but there is still work to do.
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"The manager already said we are playing with a right-back (Jeremie Frimpong) who came from the Bundesliga, is 24 years old and is trying to get used to how we defend, we play with Milos (Kerkez) who is a very young full-back, very eager and full of energy, who is trying to get used to the way we play.
"It needs time, that's absolutely normal, but we also played without our six, Ryan Gravenberch, who missed out (with suspension). We have to keep working, that's the main thing, trying to keep clean sheets.
"We conceded two goals in a transition moment where we have to do better. That's what we have to work on."

Van Dijk's comments come after Palace chairman Steve Parish admitted they may be forced to sell Guehi this summer in order to avoid losing him on a free transfer next year. "We'd have to do that, of course," Parish said.
"For players of that calibre to leave on a free, it's a problem for us unfortunately. Joachim [Andersen] went [to Fulham last summer] and we couldn't afford to lose both.
"We then had another bid [for Guehi] in January but that was a different situation. We'll just have to see what happens. But, you know, it needs a new contract or a conclusion of some kind."
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