Lamps has two years left on his current deal but is looking for more cash to reflect his status as one of the Blues' top guns.
But Chelsea appear to be stalling, hoping Lamps will back down and sign an improved offer but not one that matches his valuation.
Meanwhile pressure is piling up on Chelsea to resolve the situation ahead of the club's pre-season tour of the US.
Jose Mourinho will want all his players to be mentally and physically ready for coming season, and that will include a settlement for Lampard and John Terry - another player believed to be looking for improved terms.
Reports suggest that Roman Abramovich wants the contract deals sorted quickly.
Geremi is Newcastle-bound while Khalid Boulahrouz is in talks with Sevilla over a £3.5m move to Spain.
French midfielder Florent Maluda insists he will be a Chelsea player soon despite his club Lyon's rejection of a £12m bid .