On Monday, it was reported that Stoke had made an approach for Rowett, who guided the Rams into the Championship playoffs this season before defeat to Fulham.
Derby have now moved to acknowledge the claims and say that Rowett requested permission to discuss the possibility of a switch to the Potters.
A club statement read: "Derby County Football Club can confirm that Gary Rowett has asked for permission to speak with Stoke City regarding the vacant manager's position at the bet365 Stadium.
"The club is now in discussion with Stoke regarding the matter and will update our supporters in due course."
Rowett has been at Pride Park since March 2017, with 26 wins and 18 draws coming from 60 matches in all competitions.
Stoke are looking for a replacement for Paul Lambert, who has left the Staffordshire-based outfit after relegation to the second tier.