Whelan has spent almost a decade in the Potteries, making 336 appearances in all competitions, but he could be on the move this summer.
The signing of Darren Fletcher from West Bromwich Albion is likely to see him drop down the pecking order at the bet365 Stadium and according to the Stoke Sentinel, Villa are looking to take advantage.
It has been claimed that the Championship outfit have failed with their opening offer for the 33-year-old, but they are expected to return with a second bid in the near future.
If reports are to believed, Villa have limited money to spend this summer unless they generate funds from player sales, so signing the experienced Whelan could prove to be an astute piece of business by manager Steve Bruce.
The midfielder is currently on international duty with the Republic of Ireland ahead of their World Cup qualifier with Austria.