The Daily Express is reporting that the Blues are one of three clubs keeping close tabs on the Poland international in the 2018 summer transfer window.
The same article states that Lewandowski is keen to leave the Bundesliga giants following his controversial relationship with the Bayern board.
According to the same story, Abramovich has ties to Lewandowski’s agent Pini Zahavi to give Chelsea FC a slight advantage over Manchester United and Paris Saint-Germain.
However, the Daily Express believe Bayern’s £80m price tag could prove a potential stumbling block given the west London side’s reluctance to splurge huge transfer fees in recent seasons.
Lewandowski established himself as a top European striker after he fired Borussia Dortmund to two Bundesliga titles, the German Cup and the Champions League final under Jurgen Klopp.
The prolific goal-scorer moved to Bayern from Dortmund in 2014 and Lewandowski has scored 151 goals in 195 games over the past four seasons at the Allianz Arena.
Lewandowski has won four Bundesliga titles and the German Cup with Bayern under Pep Guardiola, Carlo Ancelotti and Jupp Heynckes.
Chelsea FC finished in fifth place in the Premier League table last season.
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