"My goal is to stay a long time," he told reporters.
"If the president wants to extend my contract to four years that would be great. I love Santos and love to play for Santos."
Robinho arrived at the Brazilian club in a helicopter with the great Pele, landing on the Vila Belmiro pitch to a fanfare welcome from 15,000 fans.
Former Santos and Brazil forward Pele was also keen for Robinho to stay long term.
"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."
The 26-year-old asked for the move back to his first club in order to cement a place in Brazil's World Cup team.
"I have my objective of going to the World Cup and being at my best at the World Cup (in South Africa in June)," said Robinho.
"I believe this can be my World Cup," he added, referring to Brazil being favourites to lift the trophy.
"In the national team competition is very big, there are a lot of good players (and) that had me worried," he said after being handed his former number seven shirt by Santos president Luis Alvaro Ribeiro.
Robinho struggled to hold down a regular place at City after moving from Real Madrid in 2008.
"I'm not going through a good period but that's normal," he said. "I spent time injured and that affected me but with a lot of work we're going to turn things round."
Robinho took a pay cut to leave City, who paid a British record 32.5 million pounds to buy him.
The Brazilian international, who scored 83 goals in 190 matches for Santos between 2002-05, hopes to make his debut in the "classico" against Sao Paulo in the Paulista championship on Sunday.
