Per the source, the Black Eagles have made an enquiry for the Liverpool striker through intermediaries but would require Batlotelli to accept a lower salary or sign the Italian striker on loan.
Besiktas could reach an agreement with Liverpool to split the payment of his wages should the Reds accept a loan bid.
The Black Eagles would be more inclined to a loan move under their current financial situation. The Istanbul giants are under FFP investigation and must report revenues higher than spending.
Besiktas are keen on replacing star striker Mario Gomez who revealed last week that he will not be returning to the Istanbul giants following the end of his loan stay.
The Black Eagles won the league title last season and will compete in the Champions League group stages as a result.
Balotelli has been transfer listed by Liverpool and the Premier League outfit have given the controversial striker the green light to leave over the summer.