Lampard, 41, spent 13 years as a Chelsea player and would replace Maurizio Sarri, who has joined Juventus after one season at Stamford Bridge.

The Blues would have to pay the Rams about £4m if they appoint Lampard.

"With pre-season fast approaching for both clubs it is hoped this will allow Chelsea to swiftly conclude their discussions," a Derby statement read.

"The club will make no further comment until it is appropriate to do so."

Lampard embarked on his first campaign as a manager last season, leading the Rams to the Championship play-off final where they lost to Aston Villa.

The former England midfielder made 648 Chelsea appearances, winning 11 major trophies.

If he does take over, he will inherit a transfer embargo after Chelsea were given a two-window transfer ban by world governing body Fifa - a decision the club are appealing against at the Court of Arbitration for Sport.

BBC Radio Derby commentator Chris Coles

The worst kept secret in football is finally getting the conclusion many Derby County fans have feared for a long time. Such has been the clamour around Frank Lampard's return to Chelsea, and the time it's all taken, Rams fans will be pleased the circus is packing up and moving on.

That's not to say they won't be sad. It was an incredible season with some amazing memories. No-one at Elland Road will ever forget Derby's second-half performance which earned them a place in the Championship play-off final.

And then there was the bounce. Whether by accident or design, Lampard endeared himself to the Derby faithful with his bouncing. It became tradition after every significant victory. The fans loved him for it.

This whirlwind relationship is coming to an end, but when the dust settles, Derby fans will remember a man who revitalised the club and ultimately moved on to the job of his dreams.

'Super Frank's' Stamford Bridge connection

Lampard joined Chelsea from boyhood club West Ham for a fee of £11m in 2001.

He won a Champions League and a Europa League at the club, while also helping them to win three Premier League titles, four FA Cups and two League Cups.

Chelsea's title win in 2004-05 was their first in half a century and Lampard scored 13 league goals that season, including both in a 2-0 victory at Bolton that sealed the top-flight crown.

He scored 10 or more Premier League goals in 10 successive seasons for Chelsea and is the club's all-time record goalscorer with 211.

Lampard left Stamford Bridge in June 2014 and had a stint at Manchester City, where he scored six goals in 32 appearances.

He then joined New York City in Major League Soccer in the US, making his debut in August 2015, before ending his 21-year professional playing career in 2017.

Lampard won 106 England caps after making his international debut in 1999 and went on to score 29 goals for the Three Lions.

He appeared in three World Cups and one European Championships.

Analysis

Phil McNulty, BBC Sport chief football writer

Should a deal be reached between Chelsea and Frank Lampard it would arguably be the biggest gamble Blues owner Roman Abramovich has made since he took over at Stamford Bridge 16 years and 11 managers ago.

Abramovich's modus operandi when it comes to managerial appointments has been based on experience, quality and success - Avram Grant apart - with not an English manager to be seen, let alone a young and relatively unproven one.

Chelsea have had five Italian managers, two Portuguese, a Brazilian, an Israeli, a Dutchman and a Spaniard in Abramovich's reign, so the notion of Lampard stepping through the door at the club's Cobham training base is a radical departure on many levels.

And make no mistake, it would not only be a huge gamble for Abramovich, it would be exactly the same for Lampard. This would be high risk for all parties.