Fabregas is currently managing Italian side Como, where he has achieved impressive results, leading the team to a top-ten finish in Serie A after earning promotion.
Despite his success, Fabregas has not yet made a decision on his future, and it is unclear whether he will stay at Como or consider other opportunities.
Klopp is said to have personally reached out to Fabregas to discuss the possibility of him taking over as RB Leipzig's head coach, following the departure of Marco Rose in March.
Fabrizio Romano, a well-known football expert, has confirmed that Klopp and Fabregas have spoken about the Leipzig project, but Fabregas is still weighing his options.