The 27-year-old World Cup winner moved to The Riverside Stadium on transfer deadline day in January.
However, Ricardinho is yet to feature for Boro in the first team and it seems unlikely at this stage that he will be offered an extended stay.
The Brazilian left Sao Paulo earlier this season when he cancelled his contract, with the hope of earning a move to Europe.
Boro handed him a short-term deal, but he has been limited to a handful of reserve team appearances.
Corinthians, the club where Ricardinho made his name, are now hoping to bring him back to Brazil.
"The relationship of Ricardinho with Corinthians has always been excellent," said Corinthians vice-president Antonion Roque Citadini.
"There were no problems when he exited the club.
"We will see what can happen in the future."
However, one major problem for Ricardinho is that he has an agreement with Sao Paulo not to sign for another Brazilian club for up to 12 months after his contract was terminated - or if he does then he will owe them $1 million.
Ricardinho's Brazilian solicitor Rubens Pozzi also insists his future remains in England.
"Nothing exists, these things are invented," said Pozzi.
"The boy is very happy in England and intends to fulfil his contract, no transfer exists."
