The Portuguese side were on Monday standing firm on the £30million asking price.
Blues boss Carlo Ancelotti has long been an admirer of Luiz and first tried to bring him to Stamford Bridge in the summer following the departure of Ricardo Carvalho to Real Madrid. However Benfica were unwilling to bend on the £43m release clause in his contract.
Blue flag flying: David Luiz is expected to complete a move to Chelsea this week
Manchester City have also made moves to secure the player's services but failed with a £35m bid during the closed season.
The Portuguese side dismissed a £17m opening gambit from Chelsea for their prized possession this month, and now the Premier League champions hope an offer of £25million plus a player, believed to be Paolo Ferreira, will be enough to end one of the longest running transfer sagas of the campaign.
Speaking after his side thrashed Bolton 4-0 at the Reebok Stadium, thanks to goals from Didier Drogba, Florent Malouda, Nicklas Anelka and Ramires, Ancelotti said: 'He is the only signing we are trying to make but if it's not possible,nothing changes. He's a very good young player but we have not agreedanything.'
International class: 23-year-old Luiz has already been capped by his country
Roman Abramovich was keen to keep a tight grip on the purse strings but changed tact having seen his side slump from the summit to the fringes of the top four, in part due to a defensive injury crisis.
Recognised centre-backs Alex, John Terry and Branislav Ivanovic have all spent extended spells on the sidelines this season.
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