Grujic has spent the past two seasons on loan with the Bundesliga club, but Liverpool believe a third temporary move would not be in the player’s best interests.
Instead, they will look to negotiate a permanent deal for the 24-year-old, who is valued at around £20 million ($26m).
Hertha are keen to re-sign the Serbian international, with reports in Germany suggesting they would look to strike another loan deal, this time with an obligation to buy next summer. Liverpool, though, are aware of interest from elsewhere and would be unlikely to sanction such a move.
Two more Bundesliga clubs, Eintracht Frankfurt and Borussia Moenchengladbach, are keen on Grujic. Both, along with Werder Bremen, tried to sign him on loan last summer, while Champions League quarter-finalists Atalanta are another to have made enquiries.
Crystal Palace, too, are understood to have made contact with Grujic’s agent, while Aston Villa have discussed the possibility of a deal – though the Midlands club are more likely to go after Philip Billing, the Bournemouth midfielder, as they look to beef up Dean Smith’s squad.
Grujic was Jurgen Klopp’s first signing as Liverpool manager back in January 2016, joining from Red Star Belgrade in a £5m ($6.5m) deal.
He has made 14 competitive appearances for the Reds since, the last of which came at Brighton in December 2017.
Since then, he has enjoyed a productive spell with Cardiff, who he helped earn promotion to the Premier League, and then two seasons with Hertha, where he has made a total of 54 appearances, scoring nine times.
He has settled well in Berlin, moving into an apartment in the city centre, and was a key figure under new coach Bruno Labaddia post-lockdown. Hertha finished the season 10th in the Bundesliga, having flirted with relegation earlier in the campaign.
Speaking exclusively to Goal back in January, Grujic insisted he had not given up hope of forcing his way into Klopp’s plans at Anfield.
“I know it’s going to be tough,” he said. “I’m not stupid. I know that Liverpool right now are an unbelievable team, the best team in the world. So, I know that I have to be at a very high level if I want to have a chance. Next season, who knows, hopefully I am ready to jump up with the team. That is what I hope for.”
Grujic is likely to feature as Liverpool take on Stuttgart in a pre-season friendly in Salzburg on Saturday (5pm UK time).
Klopp is expected to give new signing Kostas Tsimikas his first run-out, while the likes of Rhian Brewster, Takumi Minamino and Xherdan Shaqiri will all be looking to catch the eye.
Youngsters Harvey Elliott, Sepp van den Berg, Ki-Jana Hoever and Billy Koumetio, the 17-year-old defender, should also be involved.