Sky Sports reports how the pair have both been heavily linked with moves to the Premier League, with both players out of contract with the Bundesliga outfit at the end of the season.
Gunners boss Arsene Wenger has been credited with an interest in bringing both the German midfielder and the Dutch striker to the Emirates Stadium, as Wenger looks set to spend more money on strengthening his squad in the New Year.
Meanwhile, Liverpool are also in the market for reinforcements in January, with Brendan Rodgers looking to add to his midfield and forward options at Anfield.
However, any hopes the Reds coach might have had of securing Holtby and Huntelaar's signatures, have been dealt a significant blow, following Schalke general manager Horst Heldt's latest comments.
"I have actually received no concrete enquiries for them," he told Deutsche Presseagentur. "In terms of Lewis Holtby, I feel we are in a final phase (of contract talks). A decision could be quite close as it seems to actually be just about details.
"A decision could still be taken after the end of this current calendar year."
Asked specifically if there was any truth in Liverpool or Arsenal's reported interest in the two players, Heldt added: "I am not expecting to get to know any interest from any other club before the newspapers.
"I would still only consider anything after having received a concrete enquiry. Our main goal is to sign new deals with both players. We want both of them to stay on at Schalke."