Begiristain spent two days in South America to open discussions to buy the 20-year-old striker at the end of the season, which would be a bold shake-up to their strike-force and raise further question marks over the future of Mario Balotelli.
According to the Telegraph, Manchester City is aware that they will face strong competition from Barcelona should Neymar's club Santos finally be persuaded to sell.
Chelsea and Real Madrid have also previously thought they had agreements to sign Neymar, who is valued at around 32 million pounds, only for the deals to stall, the report said.
According to the report, there is pressure on the player to remain in Brazil until after the 2014 World Cup, but Manchester City have been encouraged that Santos might sell next summer and Begiristain felt that by flying to Sao Paulo he would reinforce their intent. (ANI )