The Blues see the attacking midfielder as the last piece of their jigsaw for the front half of the team.
Havertz is wanted by other clubs, and Bild journalist Christian Falk reports Leverkusen have set the 28th of August - the start of preseason training - as a deadline to complete the move.
The Bundesliga club wants Havertz focused on the coming season if a transfer does not go through.
Now it is up to the Blues to make an offer that the German club considers good enough.
Multiple sources in Europe have indicated Havertz has all but agreed personal terms and is happy to move to Chelsea.