Neville's winless streak in La Liga since taking charge last month stretched to eight matches with a 1-0 home defeat to Sporting Gijon earlier in the day.
Los Che also face the daunting task of meeting European champions Barcelona in the semi-finals of the Copa del Rey in midweek.
Siqueira, 29, has made just seven appearances for Atletico this season having been usurped in the pecking order at left-back by fellow Brazilian Filipe Luis's return to Los Rojiblancos from Chelsea.