The 45-year-old has established himself as one of Europe's outstanding young managers with back-to-back Bundesliga titles but, more than that, it is the vibrant attacking football that his team play which has caught the eye of Roman Abramovich.
Klopp rebuffed the Russian's tentative interest last season, though, signing a new contract at Dortmund to 2016. And, it remains unlikely that he would want to take the Chelsea post at the present time with an expectation that he is keen to eventually succeed Joachim Low as coach of the German national team.
They will be intrigued to see how Dortmund fare in the next round of the Champions League, when they face Shakhtar Donetsk in the last-16, who progressed from Chelsea's group, at the holders' expense.
Abramovich's more immediate concern is the team's current form, with serious questions now being raised about Rafa Benitez. The Spaniard is admired by the Blues owner, who likes the way he's gone about the task of succeeding Roberto Di Matteo in November, but knows that results cannot continue to deteriorate.
Chelsea are still clinging on to third place in the Premier League table, with the minimum requirement for Benitez to secure Champions League qualification this term.