The 24-year-old winger has previously been linked to Liverpool and RB Leipzig.
The Bundesliga club claims Villa is the team with the greatest interest in concluding a transfer before the window closes.
"They got in touch, yes, I can confirm that," Clemens Fritz, the head of professional football at the club explained to NDR-Sportclub.
"There is nothing concrete. There are a couple of requests for him. We're in intensive and close communication with his management."
Rashica is in his second season at the club, and reports in Germany have suggested that Werder want at least €20 million for the player, while Villa have only offered €18 million so far.