The Villans could recoup the money they paid for the striker.
Ayew scored seven goals in total last season
Ayew is said to have been the subject of enquiries from West Ham United, Bordeaux and Galatasaray following Villa's relegation to the Championship.
However, new owner Tony Xia insisted the Ghanaian would be staying put in a Twitter post over the weekend.
I read carefully&thanks for many ways.BTW Ayew will stay as I. I trust RDM too and he is confident to a good squad https://t.co/UxV8PVfWZv— Dr. Tony Xia (@Dr_TonyXia) July 17, 2016
That said, Hamburg's offer would allow Villa to recoup the money they paid for Ayew a year ago, and is generous considering the 24-year-old's goal return, which was slightly better than one every five matches last season.
Last month, Xia told the Birmingham Mail a new striker was "a priority" for Villa, and the sale of Ayew would increase the club's need for attacking reinforcements.
New Villa owner Xia
The former Lorient player isn't the only Villan said to be attracting continental interest, with the Sun reporting the exits of Carlos Sanchez and Jordan Veretout to Marseille as "close" on Monday.
Veretout could follow Ayew out the Villa Park exit door
The tabloid also claims that Villa have been offered £4.5 million by local rivals West Bromwich Albion for defender Ciaran Clark.
Clark is also a wanted man it seems