Last week, Bayern Munich confirmed their interest in the 22-year-old and reports have claimed that the German champions are close to agreeing a deal.
But SFR Sport claim that Liverpool remain in contact with Goretzka’s camp and are trying to persuade the midfielder to reject Bayern.
The report also claims that Liverpool have made the signing of Goretzka their top priority for the January window and they will not be submitting a major offer for Monaco’s Thomas Lemar.
Liverpool had attempted to sign the France international in the summer but their offer was rejected by Monaco.
The Ligue 1 champions have also insisted that Lemar will not be sold this month and will be kept until the end of the season.
Liverpool have also been linked with a move for Kevin Strootman, although reports claim that talks to sign the Roma midfielder are in the very early stages.
Goretzka, meanwhile, is out of contract at the end of the campaign and would be able to leave Schalke on a free transfer.
‘Leon Goretzka is a great player, that’s clear,’ Bayern’s sporting director, Hasan Salihamidzic, said last week.
‘He is a Schalke player and we obviously respect that.
‘But he is a Germany international and we can say that we are interested in him.’