Lampard is being lined up by Chelsea as their replacement for Juventus-bound Maurizio Sarri.
The former midfielder is believed to be keen on a return to Stamford Bridge and would find it nearly impossible to turn them down.
However the Telegraph are reporting that Derby have opened talks over a new deal for Lampard and that they want to keep him.
Chelsea would have to pay around £4m to buy Lampard out of his deal. But they are not giving up lightly and will try and keep their boss.
Derby reached the playoffs under Lampard, only to miss out on promotion after losing to Aston Villa at Wembley.
Lampard impressed in his first year of management, although some have questioned the wisdom of a return to Chelsea so early.
Former midfielder Craig Burley branded it nonsense while Dennis Wise called it a huge risk.
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