Despite their reluctance, Rovers granted permission after Derby triggered a £500,000 compensation clause.
Eustace, currently guiding Blackburn to sixth, remains Derby's top target following Paul Warne's dismissal.
A Rovers statement read: "The club is extremely disappointed by John Eustace's request to hold discussions with another club at such a crucial stage of the season, but this has now been reluctantly granted.
"With significant investment being made during the January transfer window...the board and ownership feel the club are in good position to challenge for one of the play-off places this season.
“With the squad bolstered, key players returning from injury and Rovers currently in a strong position in the Championship, the club and players remain focused on achieving the best possible outcome this season."