Le 10 Sport says Fla are emerging as a January option for Neymar.
The Brazil international was offered to Manchester City last week before the market shut, while Chelsea were also in contact.
And Fla vice-president Marcos Braz has stated: "I think the specific case of Neymar is now out of the question when analysing the market. Now a World Cup is coming and if Neymar wins and says, 'I'm going to live in Brazil for six months. I want to play for Flamengo'.
"If he makes this gesture, it is possible. If he doesn't, I say it's impossible."
Braz also said of the former Barcelona star: "The player has to give up a lot to play in Brazil. It's not that I want to minimise the great signings of the time, but today there are more barriers in the market."