Klopp’s side prop up the Bundesliga after suffering their eighth league defeat of the season on Sunday, going down 2-0 at Eintracht Frankfurt.
The 47-year-old is one of the most highly-rated coaches in European football and would have no shortage of suitors should he leave his position.
Asked if he had any thoughts of quitting, Klopp said: “I understand that journalists have those thoughts, but there is no such trend. I see myself as responsible.
“If it is only about luck and a change of coach can bring that, you only have to call me up and I will step aside.
“But it is not so simple. As long as nobody comes and says to me, ‘we have someone who does it better’, then I cannot go.
“I won’t stand in the way, but I cannot go before there is a better solution, the responsibility is great and I can accept it.”
Dortmund’s defeat was a result of some comically bad defending, particularly for the second goal when a terrible mix-up between defender Matthias Ginter and goalkeeper Roman Weidenfeller let in Haris Seferovic.
On the second goal, Klopp said on the Dortmund website: “It belongs in our cabinet of curiosities.”
Despite propping up the standings, Dortmund are only a point off fourth-bottom Freiburg and only 10 away from the top four.
But sporting director Michael Zorc said they were firmly in a relegation fight.
“We are in the middle of a relegation battle, everyone has to be clear about that,” he said.
Next up for Dortmund is a home clash with Hoffenheim on Friday.