Speaking to ESPN Brasil, Fluminense sporting director Fred said: "Thiago Silva has been a dream of ours for a long time, the president talks to him almost every week. Thiago has a contract in England, we're rooting for him.
"I personally am a friend of his, I'm a big fan of his character, he deserves all the best. He knows that here the doors are wide open for him to return. There's nothing [imminent]. We have to be careful not to put pressure
"The fans here all love Thiago, we love Thiago of course, and I know that Thiago loves Fluminense. One day it's inevitable, it will happen, it's the player's wish, the club's wish and we hope it happens as soon as possible."
39-year-old Thiago Silva, who is no longer a first-team regular at Chelsea under Mauricio Pochettino, is out of contract at the end of the season.
The veteran centre-back actually started his professional career with hometown side Fluminense before returning there between 2006 and 2009.
