Brazilian side International have made an approach to Manchester United regarding a January move for Anderson, according to reports in Brazil.
Sir Alex Ferguson signed the midfielder – alongside Nani – in the summer of 2007 for £20m after the Brazilian garnered a reputation as one of the most promising talents in Europe during his spell at Porto.
But although he had a decent start to life in the Premier League, Anderson has become one of the club's most disappointing transfers.
After spending last season on loan at Fiorentina, he was expected to join them on a permanent basis last summer but the deal broke down and Anderson remained at Old Trafford.
The former Porto star has struggled to overcome the situation under manager Louis van Gaal, making only two appearances for the first team this season.
In a new book released by agent Jorge Mendes, Anderson suggested he was still happy at Old Trafford and claimed injuries have prevented him from making the impact expected.
He said: "The first four years were fantastic and then an injury set me back. I was very sad and it was difficult for me to recover. This year, I am working really hard to try and regain the confidence of the coaches, because I have a lot of love for this club. I really like Manchester, I've spent a long time here and the fans have a lot of affection for me."
But ESPN.com.br reports Anderson could be leaving Old Trafford as Brazilian side Internacional are in negotiations with United to secure his services before the current transfer window closes.
According to reports, the midfielder's former club, Gremio, were also interested in bringing him back to Brazil but were put off by his high salary.
Nevertheless, the Brazilian reports claim Anderson wants to return to his homeland to be with his family as his mother is ill.
The reports add that should United fail to agree his departure, Anderson will leave the club at the end of the season for free, as his contract at Old Trafford expires in the summer.