The report states that the Germany international will sign a three-year deal with the Istanbul Giants keeping him in Istanbul until July 2018.
NTVSpor go onto say that talks between Galatasaray and Podolski have been on-going for the past two weeks.
Galatasaray are however yet to agree a transfer fee with Arsenal for the World Cup winners services.
Galatasaray sporting director Cüneyt Tanman has confirmed earlier this week that the Arsenal striker Lukas Podolski is a transfer target.
“We are interested in Podolski,” Tanman told TRT.
Podolski is expected to leave Arsenal this summer after fallout of of favour with Arsenal boss Arsene Wenger. The 30-year-old spent the second half of last season out on loan at Inter Milan.
Galatasaray will compete in the UEFA Champions League group stages next season after securing their 20th title win.