Despite leading his side to the brink of a Champion League quarter-final berth following their 1-0 win over FC Porto in the first knock-out round, Slomka is under intense pressure after dropping out of the Bundesliga's top three.
Consecutive defeats to Bayer Leverkusen and VfL Wolfsburg have seen Schalke slip down to fifth and the Royal Blues advisory board have met to discuss Slomka's future in the role.
"I will fight to the end, I want to prove I am the right man for the job despite all that has happened," Slomka told German tabloid Bild.
The 40-year-old says he has given no thought to resignation.
And with his side taking on Bayern Munich in the Bundesliga on Saturday ahead of their trip to Portugal to face FC Porto next Wednesday, wins in both games would drastically reduce the pressure on him.
"If we beat Bayern on Saturday, we stand a good chance of going third in the league and if we beat Porto we are in the Champions League quarter-finals," he said.
"That will make the club a lot of money and improve our international reputation."
Schalke president Josef Schnusenberg said the situation at the club was being discussed internally, adding that he had serious concerns.
And Bild have reported that the search is already on for Slomka who has been coach at Schalke since January 2006.