The 21-year-old has developed into a Germany international since joining Leverkusen from Mainz last year.
Leverkusen chief executive Wolfgang Holzhauser was quoted as saying by German news agency SID: “We were presented with a very concrete offer from Chelsea for Andre of beyond the 20 million euro mark.
“The sum was pushed back and forth between the two clubs. We ultimately chose Andre.
“Andre is very valuable for us. He has also made it clear he would like to stay with us.”