The Chelsea legend, 39, has edged towards the top job at the Rams after earlier this week claiming he is desperate to go into management.
Lampard would inherit a team who finished sixth in the Championship last season, who he calls "ambitious" and a "big club".
The ex-England ace revealed: "There's been interest from Derby, I've been speaking to them.
"I'm ambitious and I want to become a manager at some point.
"It's a big club, with big tradition and big history, which I really like.
"We'll carry on speaking when I go home and see."
Former West Ham star Lampard – who has also held talks with Ipswich this summer – will be taking over a side expecting to at least make a promotion push once more.
'I'M AMBITIOUS' Frank Lampard confirms he is in talks with Derby County about becoming manager
In 2017-18, they crashed out of contention at the play-offs semi-final stage – losing to eventual winners Fulham.
The Rams last tasted Premier League football ten years ago – suffering an horrific season, with just one win and 11 points from their 38 games, finishing dead-last.
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