The Blues are on the lookout for a new manager after Maurizio Sarri left for Juventus earlier this week.
Lampard is the favourite to replace the Italian, who guided Chelsea to a third-place finish and Europa League triumph last term.
However, Derby are determined to keep hold of a manager who led them to the Championship play-off final in 2018/19.
And the second-tier club are prepared to offer Lampard a lucrative new deal to try and keep him at Pride Park.
Derby will receive £4m in compensation if Chelsea do decide to appoint their all-time record goalscorer as manager.
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