The 26-year-old Robinho joined big-spending City in 2008 for a British record transfer fee of 32.5 million pounds from Real Madrid but has struggled to hold down a first-team place.
A loan deal was agreed with Santos on Thursday.
Mancini said he expected Robinho to return before the start of next season and have a big impact at the club.
"I spoke to him and told him that if he stayed then I would be happy, but that if he wanted to go back to Brazil then he could go," Mancini told reporters.
"It was important for him to play. He said he would go to Santos for five months and play there because of the World Cup.
"But after the World Cup he will come back here. He will come back here because, for me, he is a fantastic player with great technique. He can come back here and play every game."
Mancini could lose a second striker with Benjani Mwaruwari holding talks with Premier League rivals Sunderland about a loan move to the Stadium of Light.
"I spoke with him and he told me that if there was a chance he could go somewhere and play then he would like to go," said Mancini.
"It's important that he plays, it's right and we have a lot of strikers. But he will decide. If we wants to stay here then I will be happy because he's a good player."
