The Chile international is a target of Barcelona and is under contract with Udinese until June 2014.
'I have spoken to Sanchez,' said Mancini. '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.'
Hot pursuit: Alexis Sanchez looks close to sealing his dream move to Barcelona
Udinese, meanwhile, 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.
International class: Sanchez is preparing to play in the Copa America
'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 despite the Argentina forward recently expressing his desire to leave the club.
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 Italy this summer.
'Tevez is a good player,' Mancini added to Sky Italia. 'I believe he will remain with us.'
The 27-year-old is under contract with City until June 2014 and is a reported target of Inter Milan.
?Man City dogged in Sanchez pursuit despite Chilean admitting he dreams of BarcaSanchez snubs English interest by claiming: 'Barca can make me best in the world'Penny-pinching Barca cut back on office supplies in bid to ink ?35m Fabregas dealAll the latest Manchester City news, features and opinion
?Explore more:People: Carlos Tevez, Roberto Mancini Places: Barcelona, Spain, Argentina, Chile, Italy, United Kingdom
Source: Daily Mail
Source: Daily Mail