The Rams have endured an inconsistent run of form that has seen them move out of contention for an automatic promotion place.
West Ham are also reportedly interested in the Ghanaian international, with Villa looking to reduce their wage bill as they prepare for life in the Championship.
The Rams are currently fifth in the Championship table under a new-look management team of Harry Redknapp and Darren Wassall, and the newspaper claims that Redknapp is a keen admirer of the former Lorient star.
Ayew has struggled to flourish for the Villans in what has been an abysmal Premier league campaign, managing only six goals in 31 outings, but he has shown what he is capable of with some fantastic strikes.
His equaliser against Newcastle United at St James' Park in December gave the Villa fans a taste of the talent he undoubtedly possesses.
Derby look like certainties for the play-offs, with a seven-point gap between them and Cardiff City in seventh. They are 10 points adrift of Burnley in second so automatic promotion seems unlikely.
If Derby were to gain promotion, a potential signing of someone of Ayew's calibre would be a fantastic coup, and provide the Rams with a touch of Premier League quality that they do not currently have.
There is still a long way to go though, and the priority at the iPro Stadium will still be to lift themselves out of England's second tier before there is any talk of potential signings.