Various newspapers in Italy have tipped Mancini to move back to the San Siro after reports suggested the club had expressed an interest in the Italian.
Walter Mazzarri's position as coach of Inter has come under scrutiny after a run of four games without victory in Serie A, despite reassurances from president Erick Thohir.
Inter are fifth in the standings, 14 points adrift of the final UEFA Champions League spot with six games remaining.
But Mancini, who guided Inter to three consecutive Serie A titles between 2005 and 2008, intends to see out his contract with Galatasaray, having only replaced Fatih Terim on a three-year deal in September.
"My work here at Galatasaray will continue," Mancini said to Sporx.com.
"What is said about Inter is a lie.
"The same is true of the rumours linking me with the national team job in the future.
"I have a contract with Galatasaray and I will stay here."
Mancini is rumoured to be unsettled in Turkey with the club 10 points behind arch-rivals Fenerbahce in the race for the Super Lig title.
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