The Ivorian has been linked with a switch Liverpool in recent months, with reports circulating that he has failed to settle with Shanghai Shenhua.
The Chinese giants’ financial worries are also an issue, with another former Blues star Nicolas Anelka having left on a temporary loan deal to join Juventus.
Drogba is set to follow the Frenchman out of the exit door to link up with Galatasaray, where he will sign an 18-month contract.
It was widely believed that the 34-year-old would join AC Milan, with the Serie A side keen to draft in the experienced front-man to bolster their attacking options.
But, Gala are said to be near to completing a stunning swoop as they look to further their lead in the Turkish league.
The Istanbul club have already splashed the cash once this month, securing Dutch playmaker Wesley Sneijder’s signature from Inter Milan.
Many of Europe’s top clubs were thought to be interested in the midfielder, but Galatasaray completed an £8.6m deal last week.
It is unclear as to whether Drogba will have taken a pay cut from his lucrative contract in Asia.