Both clubs are well-connected to the Blues, whose former captain, John Terry, and all-time top goalscorer, Frank Lampard, are Villa assistant and Derby manager respectively.
And the pair currently have players borrowed from Chelsea within their ranks, with Tammy Abraham at Aston Villa and Mason Mount and Fikayo Tomori at Derby.
But reacting to rumour on Twitter these past 24 hours, it appears there is only one club Chelsea fans want Ampadu sent to, if he is to make a temporary exit.
Here is what is being said...
Give him to derby asap— unimke (@adiebenjamin1) November 6, 2018
Let's give him to Derby County.— Mbuso R. Buthelezi (@MbusoSavage) November 6, 2018
Rather we sold Cahill and kept him. A move Derby would be good for him though— Seppers (@Lowkey_Blues) November 7, 2018
Let's let him go to Mr. Lampard.— Pumelela (@Pumelelmjada) November 7, 2018
He should go to Derby I want Derby to qualify— Elemefootball (@elemefootball) November 7, 2018
Derby would be good. Mount and Ampadu in MF. Surprised no EPL sides are after him.— T Radu (@tradu81) November 7, 2018
Derby— Olaya (@Olaya93040623) November 6, 2018
Derby. He safe with lamps— YungAdonis (@yung4donis) November 6, 2018
Derby any day— Roman (@TheSpecialRoman) November 6, 2018
Ampadu, who can play comfortably in both defence and midfield, signed for Chelsea from Exeter City during last summer's transfer window.
The now 18-year-old has since appeared seven times for the Blues' first team and five times for Wales.
Despite the presence of Mount and Tomori at Derby, EFL rules state that up to four players can be loaned from any one club, as long as no more than two of those are over 23.
Would Aston Villa or Derby be the better fit for Ampadu?