Lewandowski’s agent, Pini Zahavi, wants a deal for his client to move to Stamford Bridge.
Express UK reports that the 29-year-old is also being chased by Manchester United and Paris St Germain.
The player had during the week announced that his time at Bayern could now be up having won the title four years in succession.
Lewandowski’s agent, Zahavi recently said, “Robert feels he needs a change and a new challenge in his career. The managers of Bayern know about it.”
However, the forward’s £80m price tag could prove a major snag.
Meanwhile, Zidane, who announced his resignation from Real Madrid on Thursday, could be back in the dugout this summer with Chelsea indicating interest already.
Chelsea have reportedly asked the 45-year-old if he wants an immediate return to a major hot seat, according to The Sun UK.
The west London outfit are struggling to find a new manager, having failed to land Maurizio Sarri, Carlo Ancelotti and Luis Enrique in recent weeks.