According to sources familiar with Lampard's situation at Derby, Rams owner Mel Morris has been delighted with the work the 40-year-old has done at Pride Park and is even planning to offer him a new deal to stay put.
With Lampard in charge, Derby came close to securing a place in the Premier League for the 2019-20 season, narrowly losing 2-1 to Aston Villa in the play-off final at Wembley.
And the former Chelsea midfielder continues to be the front runner to replace Maurizio Sarri, with early talks having already taken place.
Despite attempting to extend his contract, Derby are not expected to stand in Lampard's way if the Blues firm up their interest and press ahead with talks to appoint him as their new manager.
The Premier League club will, however, have to pay £3.5 million to buy him out his contract at Derby should they finalise a move for their legendary former player, with Sarri now all set to join Juventus.
The Serie A champions have pushed hard to complete a deal for the Italian, with the west Londoners due to net between £2.7m and £4.5m in compensation.
Chelsea director Marina Granovskaia held face-to-face talks with Juve sporting director Fabio Paratici in London last week over a two-day period and the Turin giants believe they've made decisive progress to secure Sarri.
The likes of former Juve boss Massimiliano Allegri, Ajax head coach Erik ten Hag, Wolves manager Nuno Espirito Santo, Watford's Javi Gracia and ex-Paris Saint-Germain head coach Laurent Blanc have all been considered for the top job at Stamford Bridge.
However, Lampard is the favoured candidate as the Blues prepare to have to deal with a two-window transfer ban, likely meaning they will need to make more use of their loanees and youth players in the 2019-20 season.
Chelsea opted not to ask for a freeze of the ban to the Court of Arbitration for Sport (CAS) after they were punished for misconduct in the transfers of under-18 overseas players.
The decision to not ask for provisional measures is thought to be a strategic one as the Blues continue to deny wrongdoing and have appealed the ban as a whole. Their judicial hearing isn't, however, going to be heard in time for them to sign new players.
Elsewhere at the club, Willian has not yet signed a new two-year deal despite what has been reported in the media, with the winger focusing on his commitments with Brazil at Copa America and no announcement imminent.