Chelsea were reportedly keen on bringing Klopp to Stamford Bridge in the summer but have been turned down by the impressive young coach.
Abramovich held talks with Pep Guardiola regarding the West London job also, but the former Barcelona boss opted for Bayern Munich instead.
It appears the Chelsea owner has been rejected twice in the space of a week as Klopp has his eyes set on the German national job.
The German media are eagerly anticipating the upcoming battles between Guardiola and Klopp in the Bundesliga but accept that the current Dortmund coach is in line for a move to international football.
Chelsea may now look closer to home for a new manager in the summer once Rafa Benetiz leaves his interim post with Gianfranco Zola, Michael Laudrup and David Moyes on the shortlist.