The Reds had been linked with a €12.2 million move for the Germany Under-21s international, a fee which would meet a rumoured buyout clause in his contract.
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"We will do everything we can to ensure that Emre plays for us at least one more season," squad manager Michael Reschke told the Rheinische Post.
He added to Bild: "We are convinced that another year would be right for his sporting development with us."
Can's transfer to Leverkusen included a buy-back clause which would complicate further any deal for the 20-year-old, with Bayern sporting director Rudi Voller insisting that no bid had yet been made.
"There is still no official request," Voller said of Liverpool's rumoured interest.
Can left the Allianz Arena in search of first-team football and has made 29 Bundesliga appearances in the 2013-14 campaign with Leverkusen, scoring three times.