The report states that Galatasaray have made an offer for the Germany international and will discuss personal terms with the players agent in Istanbul.
Galatasaray are understood to be preparing a three year deal for the 29-year-old.
The 28-year-old striker recently stated that he is considering his options and that he could leave on a permanent deal at the end of the season.
“I cannot confirm anything now. I have a year of my contract with Arsenal left and I have talked to others, I’m open to everything,” Podolski told Sky Sport Italia.
The World Cup winner only managed to score a single goal in 15 Serie A appearances for Inter this season.
Galatasaray won the Süper Lig title for the 20th time on Monday 25 May and guaranteed a place in the Champions League final.