The Merseysiders have been in talks about Can, a Germany Under-21 international, for some time and they have now made their move.
"Until Tuesday, it was a rumour," Leverkusen chief executive Michael Schade told Bild.
"Now I can confirm that an official offer from Liverpool is received by mail."
Can has a 12million euro (£9.75million) release clause effective for foreign clubs and it is reported that the buy-back option Bayern Munich inserted into the deal which took him to Leverkusen for £4.4million last summer is no longer valid.
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