Dos Santos is struggling to secure a starting spot in Barcelona this season and is said to be on his way out of Nou Camp.
"The news is certain, but the subject is in the hands of the agent," Dos Santos's father and former Brazil international Zizinho told Mexican press.
"We would prefer much discretion until the end of the season. We will not decide, but Barca know the situation as we have had contact with sporting director Txiki Beguiristain," he added
Zizinho confirmed that his son has attracted a lot of interest from Premier League sides, but that City were favorites to land him.
"Other English clubs have demanded information about Giovani but the main chance is City," he added.
Dos Santos, who is born to Brazilian parents but holds the Mexican nationality, still has three years left on his contract with Barcelona, who are said to be willing to let him go for a sum of 10 million euros.
"Our objective now is for him to finish the season with Barcelona at a good level and then we will speak," Zizinho concluded.