Many players are being linked with the Anfield club as they prepare for life back in the Champions League.
Liverpool will need to strengthen if they are to compete in Europe's elite club competition, and the potential loss of Suarez will further complicate matters.
Here are some of the latest transfer news and gossip for Brendan Rodgers' summer targets:
Southampton defender Dejan Lovren looks like he will force through a move to Liverpool after speaking about his thoughts on joining the club.
Lovren has told Sportske Novosti, via ESPNFC, that his "head is already at Liverpool" and that he will now sort his future out.
He said, per ESPN:
Liverpool sent the offer and the club haven't informed me. Not even about the subsequent Liverpool bids. That wasn't right. I found out about the bid from other people which disappointed me and I realised I've got no business staying at Southampton.
Liverpool is one of the biggest clubs in the world. Only Real Madrid have as many fans around the world. The last time I played at Anfield, I got chills when I heard 'You'll Never Walk Alone.' I would like to listen to it all the time.
Liverpool had recently submitted an offer of £18 million for the player, but this was rejected by the south coast club.
Pete O'Rourke from Sky Sports tweeted and confirmed Southampton's refusal:
The 25-year-old had a sensational season for the Saints last year as they finished high in mid-table. The Croatian has since won many fans and is the type of defender that the Anfield club is craving.
Lovren played 31 times for Southampton in the Premier League in 2013-14, per WhoScored.com, and played three times for his country at the World Cup finals in Brazil.
Liverpool's main weakness last season was their defence, and reliance on Suarez and Daniel Sturridge to outscore the opposition was their main tactic.
Buying Lovren would balance this point out and give the Reds a firm platform to build for the future. Even if Liverpool do lose Suarez in the next few weeks, it is vital that Rodgers performs surgery on a back four that conceded more goals in the league than Crystal Palace last year.
After his eye-catching performances at the World Cup saw him leapfrog Romelu Lukaku for Belgium in their first team, Liverpool have now turned their attentions to the player.
Moxley continues that Rodgers hopes to acquire the player from Lille by loaning him back to his club for a season, making the transfer more appealing to the French side.
But Jurgen Klopp will challenge hard for Origi as he looks to boost his squad in the knowledge that the player could favour a move to Germany, per Moxley.
Origi is a talented young individual who has been one of the surprise performers at the World Cup. The fact that he was preferred to Lukaku shows the potential that he has. But he is inexperienced at the highest level and is certainly a long-term developmental target for the Reds, rather than an impact transfer.
After being released by Chelsea after eight years of service, Liverpool are to make an 11th-hour bid to bring Ashley Cole to Anfield.
Rob Shepherd of Mail Online says that Rodgers will attempt to sign the player but that Cole is likely to leave the Premier League for a move abroad.
Shepherd writes that Cole is the target of Serie A club Roma and that the team hope to announce the deal in the near future.
Cole would be an interesting purchase by Rodgers, and a clever one at that. Despite not playing much for Chelsea last season, he is still a very able full-back and could add something to the squad dynamic as the club ventures into Europe.
The fact that Cole is on a free transfer would also help stretch Rodgers' budget and allow him to focus on other targets that he wants. Liverpool need to bring in quality as well as experience, and Cole would fit the profile well.
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