The Chile international is a target of Barcelona and is under contract with Udinese until June 2014.
"I have spoken to Sanchez," said Mancini to Sky Italia. "He said he was open to the idea of coming to City but then we have pulled out (of negotiations). After our last offer, we are out of the race to acquire the Chilean player."
Udinese confirmed the 22-year-old winger would prefer a move to Spain rather than England.
"Have City pulled out of the race?," Gino Pozzo, son of Udinese owner Giampaolo Pozzo, said to Corriere dello Sport. "You should ask them. We have not entered negotiations with City.
"The will of the player is to go to Barcelona. The negotiations with the Catalan club are going forward. With calmness, we will find a solution. We will speak to Barca and we will see."
Pozzo has not ruled out the possibility that Sanchez, who is valued at 50million euros (£44.95million), could remain at Udinese for a further season.
"He (Sanchez) said it yesterday and we have reiterated it in the past," Pozzo said."It is an option."
Meanwhile, Mancini is confident Carlos Tevez will remain at the club next season. Tevez, who played a pivotal role in the Eastlands club winning the FA Cup and securing a top-four Premier League finish, has been strongly linked with a move to Inter Milan. The 27-year-old is under contract with at Eastlands until June 2014.
"Tevez is a good player," Mancini added. "I believe he will remain with us."
Source: PA
Source: PA