Grujic would welcome the chance to remain in the German capital, but Hertha will face competition from both Eintracht Frankfurt and Werder Bremen, who have expressed an interest in signing the 23-year-old.
Frankfurt would welcome a permanent deal for Grujic, and have the funds to secure it having recently sold striker Luka Jovic to Real Madrid.
Liverpool believe they will be able to command a fee in excess of £25 million ($32m) for a player who made 23 appearances for Hertha this term.
An unnamed Premier League club have also enquired about the possibility of signing Grujic, who has played 14 times for Liverpool’s first team, while Atletico Madrid could make a move if, as expected, Rodri leaves for either Manchester City or Bayern Munich.
The Reds will allow Ben Woodburn to leave on loan, with Championship side Wigan Athletic among those interested. Hull City had been favourites to sign the Wales international, but the departure of manager Nigel Adkins has changed the landscape in that regard.
Both Herbie Kane and Ovie Ejaria are expected to join Woodburn in the Championship next season, with Brentford and Millwall having enquired about Kane, who spent a productive campaign with Doncaster Rovers in League One. Hibernian are also in the race.
Ejaria, meanwhile, is likely to return to Reading, where he spent the second half of last season. The 21-year-old is also interesting Blackburn Rovers.
Liverpool will allow two other youngsters, Taiwo Awoniyi and Anderson Arroyo, to train with Jurgen Klopp’s first-team at Melwood during pre-season.
Nigerian striker Awoniyi scored 10 goals at Belgian side Mouscron during the second half of the campaign, following a difficult spell at Gent. He has attracted interest from a host of clubs, notably Schalke.
Colombian full-back Arroyo also joined Gent last summer, but failed to make a single senior appearance.
Finally, goalkeeper Kamil Grabara is set to depart on loan once he is finished with Poland at the European U21 Championships in Italy. The 20-year-old finished the season with Danish side Aarhus, and has interest from Belgium and Germany, among others.