The Blues are keen to sign a new forward in the summer after struggling in front of goal all season, often deploying a false nine under Thomas Tuchel.
Kai Havertz has lead the line in recent weeks but Jorginho, who is the club's penalty taker, is their top scorer in all competitions with seven goals.
Sky Germany per Daily Mail have reported the Blues are very keen on Lewandowski and believe he could be the answer to their prayers.
His contract is up in 2023 and there is a belief he could want a new challenge in the twilight years of his career, having played in Germany since arriving at Borussia Dortmund in 2010.
The departure of manager Hansi Flick is said to have upset the Polish international and he would've liked to continue working with him.
Other clubs said to have shown interest in Lewandowski are Paris Saint-Germain and Barcelona.
PSG are ready to let Mauro Icardi depart when the window opens while Barcelona have also been linked with outgoing Manchester City legend Sergio Aguero.
Chelsea did spend big on Timo Werner last summer but he has failed to hit the ground running in front of goal.
Werner had two goals disallowed in Tuesday's 2-1 win over Leicester City and remarked how 'unlucky' he had been this season post-match.
"I think the first half particularly was the picture of the whole season for me up to now," Werner told Sky Sports per beIN Sports.
"I was, every time, close but at the end not really close. I think for me maybe [it was] the unluckiest season I have ever had and will have maybe, because it can't be worse.
"For example, the offside, okay the 10th time, I don't know how close it was, then a clear penalty for us. Of course I was surprised [it wasn't given] because for me it was a clear penalty.
"And then the first one, I want to make a header and I get a little push and put my arm out and then the ball goes exactly against my arm.
"I didn't know [it would be ruled out] because I felt a touch on my hand but didn't realise how it was.
"You see it on the picture that I get a little hit from behind and then my arm goes forward and it touches.
"Unlucky the whole season. When you have a season like this and you are so unlucky and you still in the Champions League final and maybe reach the Champions League next year, all good."
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