While owner Craig Whyte and new manager Ally McCoist are keen to hold on to the full back, the Scottish international is said to be dissatisfied with the estimated £1m-per-year proposition.
“I would never say never, but the email from Rangers said it was their best and final offer and we have declined that,” agent Ken Anderson told the Evening Times.
“It was a very good offer, but we think at this stage he is worth more.”
Meanwhile, Rangers have declined an offer of £800,000 from Bougherra for the player, who has a year left on his current contract.
Whittaker joined the Gers in summer 2007 for £2m.