Liverpool manager Jurgen Klopp has contacted Kylian Mbappe's agents with the Reds joining the race for the £100m striker, according to the Daily Mail.
Real Madrid are believed to be leading the race for the France international, with the likes of Arsenal, Manchester City and Manchester United having also been linked.
Premier League new boys Brighton & Hove Albion are interested in signing Liverpool defender Joe Gomez, the The Argus reports.
Gomez, who can play across the back-line, has yet to establish himself at Anfield and has also recently been linked with a move to Bournemouth.
Manchester United are trying to beat Liverpool to the signing of Sporting Lisbon winger Gelson Martins, says O Jogo.
Martins has a £46.5 million release clause, but Sporting would reportedly be willing to let the 22-year-old go for around £40m in the right situation.
Liverpool will target Stefan de Vrij as their new centre-back after ending their interest in Virgil van Dijk, Sky Sport Italia report.
The Reds confirmed this week that they will not pursue Van Dijk any further after complaints from Southampton, and his compatriot, currently at Lazio, is a less expensive alternative.
Liverpool's bid for Roma winger Mohamed Salah has hit a hiccup and as such they are studying other possibilities, Sky Sports reports.
Jurgen Klopp is looking at Sporting CP winger Gelson Martins, who has been valued at £40 million. In both cases, talks are ongoing.
Liverpool are ready to pay Real Madrid's £52 million asking price for James Rodriguez, according to Don Balon.
The midfielder has fallen down the pecking order at Madrid and is reportedly ready to leave after becoming frustrated with his situation at the Bernabeu.
Manchester United have long been linked with signing the Colombia international but it is now being reported that Jurgen Klopp's side are looking to nip in and steal a march on their rivals.
Liverpool are set to win the race to sign in-demand Southampton centre-back Virgil van Dijk, the BBC reports.
The article claims the Dutch defender has made it known that Anfield is his preferred destination, which will see the likes of Chelsea and Manchester City miss out on one of their main transfer targets.
Liverpool are planning talks with the representatives of Lyon striker Alexandre Lacazette, according to the Daily Express.
The France international's planned move to Atletico Madrid has fallen apart, and the Reds are keen to beat Manchester United to his signature.
Liverpool are closing in on a club-record deal to bring Roma winger Mohamed Salah to Anfield, according to the Daily Telegraph .
The Reds are willing to pay in excess of £35 million to sign the Egypt international are hopeful of completing the deal within a week.
Liverpool are continuing negotiations to sign Mohamed Salah from Roma and are also interested in acquiring forward Keita Balde Diao from Lazio, according to ESPN.
Salah remains a key target for Jurgen Klopp's side, and they are also monitoring Balde's progress in Serie A ahead of a potential bid.
Liverpool have had their opening bid of £28 million for Roma winger Mohamed Salah rejected, according to the Daily Mail.
The Reds are keen to bolster their attacking ranks this summer, but the Serie A outfit value the Egypt international at £40m.
Manchester City face stiff competition from a number of their Premier League rivals in their bid to sign Monaco defender Benjamin Mendy, according to L'Equipe .
Chelsea and Liverpool have both accelerated their interest in recent days while Manchester United are also monitoring developments.
Full-back Mendy is keen to move to England this summer, though Barcelona are also keen on the 22-year-old.
Should Philippe Coutinho depart Liverpool for Barcelona, Jurgen Klopp will seek to sign Mario Gotze from Dortmund, Transfer Market Web reports.
The World Cup winner is a favourite of the manager and worked with him previously at BVB.
Former Real Madrid captain Iker Casillas could make a summer switch to Liverpool, according to AS.
The Spanish publication suggests that the veteran Spain goalkeeper has arranged a pre-contract agreement with the Merseyside club, who return to the Champions League next season having finished in the top four of the Premier League.
Liverpool are leading the race for Arsenal midfielder Alex Oxlade-Chamberlain, according to The Sun .
The England international is looking for a new challenge after six years with the Gunners and will be available for around £20 million.
Manchester United and Liverpool have made enquiries for Monaco star Tiemoue Bakayoko, according to the Daily Mail .
The newspaper reports that the clubs are set to rival Chelsea for the services of the 22-year-old, who impressed in Ligue 1 and the Champions League this season.
Liverpool are ready to beat off competition from Everton and Tottenham to land Leicester attacker Demarai Gray, the Mirror reports.
It is said that the 20-year-old trickster has a release clause of £12 million, which the Reds are more than willing to pay when the transfer window opens in July.
Real Madrid and Barcelona could be set to battle over Liverpool teenager Ben Woodburn, according to Don Balon .
Barca have been monitoring the forward after he became Liverpool's youngest ever goalscorer earlier this season.
And now Madrid have been alerted to his talents, with fellow Welshman Gareth Bale insisting the Blancos make a move for the 17-year-old.
Real Madrid are considering a move for Gini Wijnaldum as their chances of signing Eden Hazard continue to fade, according to Tuttomercatoweb .
Los Blancos have already held a meeting with the Liverpool midfielder's agent as they look to make an impact signing to bolster their squad this summer.
Tottenham, Everton and Liverpool will all fight to sign Leciester City winger Demarai Gray at the end of the season, according to a report from the Mirror .
The Foxes attacker is growing frustrated with his lack of playing time at the King Power, having played only two full games for the club this season, and will reluctantly push for a move in the summer.
Barcelona are poised to make a bid worth up to £51 million for Liverpool star Philippe Coutinho, according to Sport .
The Catalan club are desperate to land the Brazil international this summer, but are equally keen not to upset the balance in the club's dressing room, and are thus wary of offering Coutinho a huge contract if he does move to Camp Nou.