Karius delivered another outstanding display in Schalke's 3-1 win away at Union Berlin on Friday, a week after a similarly impressive performance in a goalless draw against Bayern Munich, and was named man of the match for the second week running.
Speaking to Sky afterwards, the 33-year-old goalkeeper addressed the growing chatter around a possible first senior call-up.
"If people are linking me with that, then it's a recognition of the performances I'm putting in. That's great," Karius said. "But anything beyond that isn't up to me."
Asked whether he had already been in contact with national team head coach Jurgen Klopp, under whom he played during his time at Liverpool, Karius was clear there had been no dialogue so far.
"No, there has been no contact," he said. "I don't rate anything as realistic or unrealistic. I just keep going. Everything else will come or it won't."
Klopp is due to name his first squad as Germany head coach on 17 September, with the position of the country's number one goalkeeper considered wide open following Manuel Neuer's international retirement. Karius, who has never won a senior cap in his career, would earn a landmark first call-up should he be included.
Schalke teammates have voiced support for the idea. Captain Kenan Karaman said he hoped Klopp would extend an invitation, while Robin Gosens, who scored in the win over Union, said he wished Karius a call-up "from the bottom of my heart," aware of how much it would mean to the goalkeeper personally.
Karius' career has taken in spells at Manchester City, Mainz and Liverpool, where he became a well-known figure after two high-profile errors in the 2018 Champions League final defeat to Real Madrid under Klopp, a result that shaped much of the public perception of him for years afterwards.
He returned to Germany with Schalke last year and has since established himself as one of the Bundesliga's most improved performers, helping the promoted side to their first Bundesliga win in over three years earlier this season, a run of form that has slowly begun to shift the narrative around him.