Brazil's Globo said Razia, the 2012 GP2 runner-up, had secured the place "after months of negotiations".
"The official announcement will be made on February 5, during the presentation of the new car" at Jerez, said the report.
Razia, who linked to the report on his official website, is quoted as saying: "We have managed to close (the deal) at the last minute. The important thing is that I have got what I have worked for over 11 years, since karts.
"It really is the fulfilment of a dream for me."
Finnish newspaper Turun Sanomat said Razia has at least $15 million in backing.
"I have always raised the flag of Brazil, but we have only European investors in this project," said the driver.
Despite the Globo report and Razia's comments, the driver's management did not confirm the deal when contacted by the British broadcaster Sky.
"At the moment we have made no decision," a spokesman said.
Marussia said on Thursday that its confirmed rookie, Max Chilton, will debut the team's new MR02 car at Jerez next Tuesday, when "the rest of the testing schedule will also be communicated".
Meanwhile, a Dutch media report said Giedo van der Garde is close to securing the second race seat at Caterham, alongside Frenchman Charles Pic.