The Reds want the Serbia international to gain first-team experience next season and have received interest from a host of clubs across Europe.
Cardiff are in pole position, with Grujic having spent the second half of last season on loan with the Welsh outfit, helping Neil Warnock’s side earn automatic promotion to the Premier League. The 22-year-old made 14 appearances, though he was left out of the side towards the back end of the campaign.
Warnock is a fan, however, and was impressed by the way he handled his first extended run of games in English football. Liverpool are keen for Grujic to work on his defensive awareness, decision-making and discipline, and would ideally like him to remain in the Premier League in order to do so.
Talks have already taken place with Cardiff but both Milan and Lazio have registered their interest in a permanent deal. Another Serie A side, Atalanta, are interested in a potential loan move, while Fulham have asked to be kept informed of developments. The Londoners would consider Grujic if they were to lose their captain, Tom Cairney.
Grujic was signed by Liverpool in January 2016 from Red Star Belgrade, and is highly thought of by Klopp due to his physical and technical attributes. He has made 14 senior appearances for the Reds, though he is yet to start a Premier League game. Liverpool paid a little over £5 million to sign him, and would be unlikely to consider a sale for anything less than double that.
In any case, his future is unlikely to be finalised until after the World Cup, where he was an unused substitute for Serbia’s opening game against Costa Rica in Samara on Monday.
Liverpool are seeking loans for a number of other young talents, with Ryan Kent and Sheyi Ojo both set to depart in this window. Kent has interest from numerous clubs, chief among them Leeds and Rangers, while Ojo is wanted by Stoke, Aston Villa, Birmingham and Derby.
Allan Rodrigues de Souza and striker Taiwo Awoniyi, both of whom are yet to secure UK work permits, will also be sent out, as will midfielder Pedro Chirivella.
Allan, who is hoping to return from a shoulder injury next month, has interest from clubs in the Netherlands, Germany, Portugal and France, while Awoniyi is set to remain in Belgium, where he spent last season with Royal Mouscron. Anderlecht and Club Brugge are leading the chase for the Nigerian. Awoniyi, 20, scored 10 goals in the Jupiler League with Mouscron and will be handed a new contract by Liverpool before heading out on loan once more.
Daniel Sturridge, meanwhile, will be sold if a suitable offer is received. Fenerbahce and Sevilla are understood to be keen on the striker, who made little impact during a loan spell at West Brom last season, making just six appearances due to injury.
Sturridge’s wages, however, could prove a stumbling block. He is entering the final year of his contract, which is understood to be worth around £120,000 a week. Liverpool’s asking price is understood to be around £15 million ($20m). Inter and Newcastle were interested in the 28-year-old in January but are unlikely to return to the table this summer.
Elsewhere, Liverpool will appoint Barry Lewtas as their new U18s coach.
Lewtas has previously been in charge of the Reds' U15 and U16 sides, but will now step up following Steven Gerrard's departure. Neil Critchley will remain as U23s manager, but assistant Mike Garrity will leave the club this summer as the Academy looks to streamline staff numbers.