The Championship (second tier) club said in a statement the decision was to allow Lampard’s discussions “to be concluded as soon as possible”, Reuters reported.
“On the assumption that Frank will reach an agreement with Chelsea to become their new manager, the club shall step up its efforts to find a replacement manager,” Derby added.
Lampard won three Premier League titles and the Champions League as a player at Chelsea and is favorite to replace Maurizio Sarri after the Italian joined Serie A champion Juventus.
The former England international led Derby to the Championship playoff final last season, losing to Aston Villa, in his first year in management.
The 41-year-old is adored by the Chelsea faithful for his record-breaking goalscoring exploits during a trophy-laden 13 years in West London.
Chelsea last month appointed its former goalkeeper, and Lampard’s ex-teammate, Petr Cech as technical and performance advisor.
The club last month appealed a transfer ban imposed by world soccer body FIFA for breaching rules regarding the international transfer and registration of players under 18.
The ban prevents Chelsea from signing players in the close season and January transfer window in 2020.
The Premier League club announced on Monday that 31-year-old Argentine striker Gonzalo Higuain, who was on loan from Juventus, was one of five players to have left at the end of their contracts.
Captain Gary Cahill, retiring goalkeeper Rob Green, Eduardo and Kyle Scott were the others.
Goalkeeper Eduardo spent last season on loan at Vitesse Arnhem.