The 53-year-old Israeli, who got the push after guiding the Blues to the Champions League final two months ago, was banking on a £5million golden handshake.
But the contract Grant signed entitles him to a payout of less than £2m.
A close pal revealed: “Avram is unhappy with the offer so far and is still locked in negotiations.
“He had two years of his contract left to run and he believes he should be entitled to a bigger slice of the cake.
“He joined Chelsea because of his friendship with owner Roman Abramovich and he’s hoping he’ll sort it all out personally. He believes a handshake and a verbal offer should be enough.”
Grant only lasted nine months in charge at Stamford Bridge but guided the team to runners-up spot in the Premier League and the Carling Cup Final.
Since his sacking he has been offered the chance to manage Georgia and the Czech Republic but has turned down both.
The pal added: “He wants to continue in club management as he enjoys the cut and thrust on a daily basis but he wants to sort out the Chelsea situation first.”