Forest are very keen to sign the talented midfielder, which is why they are willing to go up to £13 million, according to Sky Sports.
The deal will be subject to a medical. Should Carvalho clear those tests, he will become a Forest player very soon.
The deal is more than double the previous transfer record at the club.
At 21, Carvalho is the right age for Forest. They see him as a player who will develop his game and help the team immensely in the coming seasons.
He may also be joined by his current teammate Diogo Goncalves, who could join Forest on a season-long loan.