The Premier League side have previously been linked with the Brazilian, but their interest is thought to have dropped in recent weeks.
Inter Milan were believed to the front-runner for his signature, after freeing up space in their squad by allowing Wesley Sneijder to leave and accepting Liverpool’s approach for Philippe Coutinho.
But, the Italians are reportedly now shelving any approach until the summer, opening the door for Chelsea to pounce this month.
The 24-year-old is seen as one of the top talents in his homeland, with a series of fine displays helping Corinthians to claim the 2012 Copa Libertadores.
His performances during their Club World Cup victory over the Londoners alerted manager Rafael Benitez, who is keen to draft in fresh faces in a bid to re-enter the title race.
Corinthians are thought to be against the idea of allowing their star man to leave, and are said to be holding out for a figure in the region of £15m.
It is unclear as to whether Paulinho is seeking a move, with the midfielder hoping to make Brazil’s squad for the 2014 World Cup.