The Brazilian side cools talk linking the striker with a move after his impressive display in Brazil's Confederations Cup triumph
With Carlos Tevez having left the Premier League for Juventus, Manuel Pellegrini is in the market for new blood up front, with Napoli striker Edinson Cavani the subject of an offer.
Fred is one of several names to be linked with a move to the Etihad Stadium due to his impressive display at the Confederations Cup, including two goals during Sunday's 3-0 final win over Spain.
Fluminense's director of football, Rodrigo Caetano, insists that the 29-year-old is happy to stay.
"Fred is under contract with Fluminense, he is very happy at the club and we are very satisfied with him," Caetano told ESPN Brazil.
The striker, who returned to his homeland from Ligue 1 side Lyon in 2009, would only have his head turned by "a really great offer".
"I am doing great at Fluminense and I will only leave the club if there is a really great offer," he declared.
The striker finished top goalscorer in the Brasileiro Serie A last season to help his side clinch its fourth title, netting 20 in 28 appearances.