Havertz is set to complete a switch to Stamford Bridge in what could turn into Chelsea's record transfer move.
The 21-year-old is expected to move from Bayer Leverkusen in an initial £70million deal, which could end up rising to as much as £90million depending on add-ons.
That will usurp the Blues' current record purchase of £71.6million for goalkeeper Kepa Arrizabalaga, who they made the most expensive stopper in world football when they bought him from Athletic Bilbao in the summer of 2018.
But Sky Sports says Abramovich did hold reservations about the Havertz deal.
They claim that the Russian billionaire wasn't happy with the initial asking price of a full £90million, and it was only when the structure of the deal was altered that Abramovich was willing to play ball.
Chelsea are now set to pay the fee for Havertz across a series of instalments, with the transfer due to be completed before the start of the Premier League season.