The Bundesliga club wanted to take the 28-year-old on loan for the season, with the offer thought to include an option to buy.
But the terms of the deal were not acceptable to Villa, who turned it down.
Despite the rejection, Buendia’s future remains uncertain heading into the final days of the transfer window.
The former record signing, who spent the second half of last season on loan at Bayer Leverkusen, was initially among the players Villa were content to move on this summer, in order to give them more wriggle room in the transfer market.
But a positive pre-season saw Buendia come back into boss Unai Emery’s plans and he made his first Premier League appearance for the club since January in last weekend’s 1-0 defeat at Brentford.
Buendia, who joined Villa from Norwich in a £38million deal four years ago, was brought on to replace the injured Boubacar Kamara but then later substituted himself in the second half.
Villa, who have been operating under severe financial restrictions in the window, will now consider any further offers they receive for the player before Monday’s deadline.