Grujic was Jurgen Klopp's first signing as Liverpool boss, but has struggled for first team action.
The towering midfielder is a full Serbia international, starting in their recent friendly with South Korea.
Liverpool should look no further than former manager Rafa Benitez, currently in charge at Newcastle United.
Newcastle's midfield was trampled all over by Watford at the weekend, with Mohamed Diame once again looking out of place in a Premier League side.
Ex-Reds star Jonjo Shelvey was not much better, and adding in an exciting box-to-box player like Grujic could add a new dimension to Newcastle's options.
Grujic has impressed for Liverpool when given chances in pre-season and the League Cup, but he has never had a sustained run of league games.
The 21-year-old would be a low risk option for Newcastle and one they should consider despite a potential takeover windfall.
Bringing him in on loan would put them in pole position to acquire Grujic on a permanent deal in the future, if Liverpool are unable to offer him the game time he needs next season.