The El Diaro Sur daily reported that the 29-year-old Brazilian has agreed a three-and-a-half-year contract with the Andalusian club on Tuesday.
Italian daily Corriere dello Sport reported that Malaga will pay two million euros for Baptista, whose annual salary will fall from 3.2 million euros to 2.5 million euros.
The final decision on the transfer rests with Italian bank Unicredit, who are Roma's majority shareholders.
Baptista, a member of Brazil's World Cup squad, made his name in Europe with Sevilla before joining Real Madrid in 2005.
He spent a season on loan at Arsenal in 2006-07 and signed for Roma in 2008, but has failed to hold down a first-team place at the Italian side.
Meanwhile, Argentine international centre-back Martin Demichelis has joined Malaga from Bayern Munich on a season-long loan with a three million euros option-to-buy clause.
Malaga are currently 18th in the Spanish top flight.