Goretzka has been likened to Michael Ballack and is Germany's most promising central midfield prospect, starring at the Confederations Cup last summer.
His contract expires at the end of the season and Goretzka is expected to make an announcement on his future next week.
Schalke could still sell Goretzka for a big fee this January, which is why it would be a stunning deal if Liverpool could seal his signature on a free transfer.
The midfielder is free to negotiate a pre-contract agreement from January 1.
Liverpool have already acted quickly this transfer window so sign Virgil van Dijk for a club record fee.
They already have Naby Keita joining from Bundesliga club RB Leipzig next summer.