Lampard has been the front runner to take over from Maurizio Sarri, who left for Juventus at the end of the season.
The former midfielder will return to his old side if he can agree personal terms after Chelsea agreed to pay his £4million release clause.
Derby released the statement on Twitter.
“Derby County can confirm that they have granted permission for Chelsea to speak to Frank Lampard about the vacant managerial position at Stamford Bridge,” they wrote.
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“With pre-season fast approaching for both clubs it is hoped this will allow Chelsea to swiftly conclude their discussions.
“The club will make no further comment until it is appropriate to do so.”
Lampard has only been in his maiden managerial role at Derby for 12 months.
However, he guided the Rams into the Championship play-offs at his first attempt.
Derby were on the verge of a return to the Premier League but they lost the play-off final against Aston Villa at Wembley.
Lampard is thought to wait a number of assurances from the Blues board before he returns to Stamford Bridge.
With a two-window transfer ban looming, Lampard will need to put his faith in the academy stars.
Chelsea youngsters Mason Mount and Fikayo Tomori flourished on loan at Derby last year under his stewardship.
Similar young players will need to be given an opportunity in a vast shake up of the club’s policy.
Rarely have the Blues thrust any academy graduates into their first team since Roman Abramovich bought the club in 2003.
But Lampard spent 13 years at the west London club and has extensive knowledge of the set-up.
The 41-year-old is also expected to demand time from the board to allow for progression while under a transfer embargo.
Lampard will be joined by former team-mate Petr Cech, who left Arsenal to become the new Technical and Performance Advisor.
Jody Morris, Lampard’s assistant at Derby, is expected to follow the boss to Chelsea.
The pair will have a big rebuilding job, especially after star man Eden Hazard left for Real Madrid.
Gary Cahill has also left the club as a free agent, while Bayern Munich are keen on signing Callum Hudson-Odoi.