Manchester United have been heavily linked with a move for the 23-year-old Monaco star, who was instrumental in helping his side win the Ligue 1 title and reach the semi-finals of the Champions League last season.
Recent reports suggested Fabinho looks to be staying put at Monaco, with United cooling their interest.
However, according to Spanish paper AS, Atletico Madrid are closing in on a deal, with a fee of around £40million agreed.
It is said a deal in principle has been reached for the player, who can operate as a right-back or defensive midfielder.
This is despite the La Liga giants being unable to buy or sign players due to the transfer ban they are serving.
Atletico frustrated United last month when they tied Antoine Griezmann, who was previously Jose Mourinho’s top striking target, down to a new long-term contract.
AS also claim Fabinho’s former club Real Madrid will profit from the prospective deal, pocketing £200,000 from the transfer.
Despite missing out on Fabinho, United are expected to carry on being active in the transfer window.
They took their summer spend past the £100m mark with the signing of Romelu Lukaku from Everton.
The Red Devils are currently on a pre-season tour of the United States and Lukaku is training with his new team-mates.