Former Leicester manager Nigel Pearson
And the 52-year-old, also a reported target for hometown team Nottingham Forest, is said to have impressed the Rams' board.
Derby have failed to secure promotion to third season running, losing to Hull City 3-2 on aggregate in the semi-finals of the play-offs.
Derby's Chris Martin and Johnny Russell look dejected
And the report claims the Rams, who are also planning to interview interim head coach Darren Wassall, hope to have a permanent appointment in place as early as next week.
Pearson, who had spells in charge of both Southampton and Hull, is best known for his time at Leicester City, with whom he won two promotions - the latter of which to the Premier League.
The former Foxes boss celebrates with Chairman Vichai Srivaddhanaprabha and Vice Chairman Aiyawatt Srivaddhanaprabha during the promotion parade
However, the former Sheffield Wednesday captain, who still lives in the Steel City - approximately 40 miles from Derby, has been out of work since leaving the King Power Stadium a year ago.
According to the Telegraph, Pearson has also spoken to Aston Villa and Fulham in that time.
Birmingham City boss Gary Rowett and out of work pair Roberto Martinez and Tim Sherwood are also said to be under consideration by the Rams' board.
Former Everton manager Roberto Martinez