It is claimed that a £4.4million package has been agreed with the 18-year-old's current employers Fluminense.
Chelsea already own a 40% stake in the talented youngster and were granted first option on his services after allowing Deco to join Fluminense in 2010.
With Serie A giants Juventus, Napoli, Udinese and Inter Milan now said to have joined the hunt for Wallace's signature, and with Manchester City monitoring his progress, Chelsea have decided to make their move.
It is reported that Wallace will not join up with the Premier League outfit until next summer, with the youngster set to be loaned back to Fluminese once an agreement is completed.
He will then join the ranks at Stamford Bridge in June 2013 and compete with Branislav Ivanovic and Cesar Azpilicueta for a right-back berth.
Wallace's agent has admitted in the past that a move to Europe is something he and his client have considered, but Fred Moraes has refused to comment on the latest Chelsea reports.
He told Lancenet: "I can't talk about this subject."
Fluminese are, however, prepared to talk up the their young star, with coach Abel Braga of the opinion that he is a brighter prospect that Mariano - who was offloaded to Bordeaux in 2011.
Braga said: "This kid has an extraordinary future ahead of him.
"He is a replica of Mariano but does not have the personality of him yet. But in the attacking third of the field, his level of crossing is superior to Mariano."
Should Wallace make a move to Chelsea, he will join fellow countrymen David Luiz, Ramires, Oscar and Lucas Piazon, who was part of the same Brazil U17 side at the 2011 World Cup in Mexico, in west London.