The 21-year-old has established himself as one of Germany's most exciting young talents since joining Leverkusen from Mainz last year.
Leverkusen chief executive Wolfgang Holzhauser told 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."