The former Manchester City and Inter boss took over from Fatih Terim in September last year, guiding the club to a Turkish Cup win as well as second place in Super Lig.
There had been speculation in some quarters that Mancini felt inclined to return to his homeland, but the 49-year-old has insisted he is happy in Istanbul.
"I miss Italy, not only in affection but also for the football," he told Gazzetta dello Sport.
"But I will be clear - I am staying at Galatasaray. I have two years on my contract and I am fine.
"We will play in the Champions League, we will resume in mid-July."
Mancini also took time to discuss potential transfer targets, revealing that some had already fallen by the wayside.
"What do I need? A defender, for the back four, a striker, a winger," he added.
"From Italy who would I sign? People with experience, and in Italy there are so many who could be useful in Turkey.
"(Fabio) Quagliarella and (Davide) Astori? I like Quagliarella a lot, he can shoot, he has talent.
"We tried to sign Astori in January. Just as we had gone in now for Alex and (Seydou) Keita, but they went to Milan and Roma."
