Lampard is keen to stay at Chelsea but feels his service over the past seven years means he should be the club's highest-paid player.
Skipper John Terry currently holds that honour on £130,000 a week with Lamps on around £100,000.
Lampard's advisors talked with Chelsea chief executive Peter Kenyon over the last 24 hours. But the club's new offer came nowhere near what they want.
The Blues insist they will go no higher and have given the £11million buy from West Ham star just a few weeks to consider their proposal.