"My goal is to stay for a long-time," the 26-year-old said. "If the president wants to extend my contract to four years that would be great."
Robinho, who has re-joined his first club on a six-month loan, arrived by helicopter with Brazilian legend Pele.
Some 15,000 fans turned out at the Vila Belmiro stadium to greet the star duo.
Pele, who scored 474 goals for Santos, is also keen to see Robinho extend his loan period.
"I hope this passage is not merely for a few months but that it's permanent," said the club's biggest idol. "I hope Robinho recovers (his form) for Santos and the national team."
Should Robinho make his transfer permanent?
Robinho, who cost a British transfer record £32.4m when he arrived at City from Real Madrid in 2008, is hoping to secure his place in the Brazil side for the World Cup after falling out of form and favour at Eastlands.
"I have my objective of going to the World Cup and being at my best at the World Cup," said Robinho, after receiving his former number seven shirt from Santos president Luis Alvaro Ribeiro.
"I believe this can be my World Cup. In the national team competition is very big, there are a lot of good players and that had me worried."
Robinho, who scored 83 goals in 190 matches for Santos between 2002 and 2005, hopes to make his debut in the "Classico" against Sao Paulo in the Paulista championship on Sunday.
Source: BBC Sport