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.