The Reds are in desperate need of midfielders having seen Jordan Henderson and Fabinho depart for Saudi Arabia this summer.
Moises Caciedo and Romeo Lavia, both Liverpool targets, have picked Chelsea, though the Merseyside club are set to snap up Wataru Endo.
Manchester United also want a midfielder and, according to French outlet Foot Mercato, the Red Devils and Liverpool are back in the hunt for Gravenberch.
Gravenberch is not pushing to leave Bayern Munich, but he could again struggle to command regular game time if he stays put.
He joined the German giants last summer from Ajax for an initial €18m fee, however, he only played a bit-part role for them last term.
The Dutchman does have a preference if he is to move though and it is claimed to be Manchester United over Liverpool.
Moving to Old Trafford would see Gravenberch given the chance to play in the Champions League, something Liverpool cannot offer.
