The Bundesliga club have denied reports the Cameroon international, whose contract runs out in June, is on the verge of leaving for Jurgen Klopp's side this month
As reported by Goal on Wednesday, the Reds have not yet concluded a pre-agreement with Matip - whose contract expires in June - but are confident he will join them in the summer.
Liverpool had initially attempted to prise the 24-year-old centre-back away from Veltins-Arena this month, but are content to wait until the end of the season.
However, rumours persisted in Germany that a January exit could still be on the cards - something Tonnies has laughed off.
READ MORE | Matip expected to join Liverpool in the summer
"Matip to Liverpool this month? That's a hoax," the Schalke supremo told Sport1.
The defender is a product of the Schalke youth academy and has developed into an important first-team member in Gelsenkirchen since making his official debut in November 2009.
Matip has made 18 Bundesliga appearances this campaign, scoring three goals in the process.