Manchester United have been linked with the Dutch playmaker for most of the summer but attempts to sign Sneijder have floundered because the overall financial package is just too great.
Over the past 24 hours a number of rumours have surfaced suggesting City may exploit United's difficulty and swoop for Sneijder themselves.
However, immediately after his side's 3-2 Community Shield defeat to United at Wembley, Mancini rejected claims he was about to raid his former club.
"No," he said. "It is not true.
"He is an Inter Milan player. We never spoke about him."
It means Old Trafford is the only likely destination for the 27-year-old, whose future is set to be decided next week according to Inter coach Gian Piero Gasperini after the 2-1 Super Cup defeat to AC Milan in Beijing.
"As for the rumour of Sneijder leaving, we will talk about it next week," said the 53-year-old.
Sneijder has broken his silence over his future.
"All I know is that Inter need money and that I'm for sale if the right offer comes in," he told Voetbal International.
"I have five days off after the international friendly against England on Wednesday. I expect clarity on my future by then."
"I can be very brief about the interest from Manchester United and City: I haven't spoken with either of those two clubs, so I can't really say much about my future at the moment."
Meanwhile, Mancini has confirmed he expects Carlos Tevez to begin training on Monday after a three-week break following Argentina's exit from the Copa America, with sources close to the player stating he is in Manchester.
"Yes. I expect Carlos to be back (on Monday," said the City chief.
Source: Team Talk
Source: Team Talk