Currently on loan at Rayo Vallecano, the 19-year-old has caught the eye of several top Premier League clubs, including Chelsea, Arsenal and United.
The Spain under-21 star had his representatives meet with Arsenal boss Arsene Wenger earlier this month, while Chelsea and United officials have watched him in action for Rayo Vallecano.
Phil Neville took a trip to Spain last weekend following a glowing report from United chief scout Robbie Cooke.
Chelsea officials have also been in the stands at the Campo de Futbol de Vallecas.
But the Premier League giants will have to pay £20m to land the midfielder, the price inserted into Niguez's Atletico Madrid contract that allows him to talk to other clubs.
The report also states that Niguez may himself put pressure on Atletico to allow him to talk to United or Arsenal should either make a bid that falls short of triggering the £20m release clause.