Citizens boss Manuel Pellegrini is keen to bolster his defensive options in the summer and has identified Alves as the man to help his side become a force in Europe.
Current Manchester City right-back Pablo Zabaleta has been one of the most consistent performers in the Premier League this season, however Alves would add more to the side going forward.
Alves, who joined Barcelona from Sevilla back in 2008 for an amazing £23.5million.
The Brazilian international has gone onto become one of the best full-backs in world football - winning four La Liga titles and two Champions League medals since moving to the Camp Nou.
Reports suggest Alves has a £40million buyout clause inserted into his contract, however Manchester City are prepared to accept an offer in the region of just £15million for the 30-year-old as they are looking to raise funds in order to improve their stadium.