This recent report from the Daily Mail claims that a deal between the two sides is imminent.
According to other claims made in the report, Chelsea have been chasing the 18-year-old Brazilian since March.
Wallace helped Fluminense clinch the 2012 title in the Brasileiro with one match left in the Brazilian top flight season.
Wallace spent his youth career in the Fluminense system and made his first-team debut in 2011 at the age of 17, something that is more of a regularity in South America than in Europe unless you are the next Lionel Messi. The 2012 season, which runs from May to December in Brazil, was the first full season for the right back and he has done enough to earn the attention of Chelsea and sign a potential contract with the club.
If he were to join the Stamford Bridge club, Wallace would be the fifth Brazilian on the roster with David Luiz, Oscar, Ramires and Lucas Piazon all at the club currently.
The right back position at Stamford Bridge is currently occupied by Branislav Ivanovic, 28, and Cesar Azpilicueta, 23, with Azpilicueta being the player who will play that position for the foreseeable future as Chelsea continue their youth movement.
Wallace could be sent on the path that is being used at the moment for goalkeeper Thibaut Courtois and midfielder Kevin De Bruyne as a young signing being sent out on loan to gain more experience instead of sitting on the bench at Chelsea.
This report from Goal.com states that will be the case with Wallace as he will go back to Fluminense on loan.
This is definitely a move for the future as Wallace would not get playing time in the first team immediately if he completes his move to Stamford Bridge.