Per the source, Talisca will arrive in Istanbul imminently to undergo his medical and sign his new deal.
The latest developments follow the €7.5 million sale of Jose Sosa to AC Milan which went ahead on Wednesday.
The Black Eagles would have beaten off competition from Liverpool and a massive £20 million bid from Wolves if the deal goes ahead as planned over the next few days.
The Sun reported that Wolves were nearing a £20 million deal with the 22-year-old following their takeover by Chinese investors Fosun in what would have been a marquee signing.
The tall Brazilian midfielder has 20 goals and four assists in 78 appearances for the Portuguese giants in all competitions.
Besiktas are expected to have a busy week in the transfer market signing another defender and most importantly a replacement for striker Mario Gomez who joined Wolfsburg on Wednesday.