A deal would involve Bafetimbi Gomis replacing the former Palace, Spurs and City striker in Turkey.
Gomis has been on loan at Marseille over the past season, scoring 21 goals in his 33 appearances in all competitions.
But he is understood not to have a future under Paul Clement in Wales.
Adebayor joined Istanbul Basaksehir in January and helped them to finish second, reaching the Champions League. But he wants to return to England.
The 33-year-old scored six times in 11 appearances for Basaksehir this year, including a stunning hat-trick in his side’s 4-0 thrashing of Turkish giants Galatasaray.
Earlier this week, Adebayor claimed joining his last Premier League club, Palace, was one of the worst decisions of his career.
The 33-year-old striker, who famously revealed he had to Google the club to find out who they were, insisted he only joined to appease his advisers.
Adebayor said: “I had some great experiences in England in clubs who are among the best in the country.
“The only error that I made was to sign for Crystal Palace in January 2016.
“I did it just to please my entourage, who were saying to me: ‘Manu, you have to start playing again!’ It was the worst decision of my career.”