It follows a similar report from Radio Marca on Friday that said the finishing touches were now being put in place on an agreement, which may be announced as early as this week.
The Chilean is well known within Spanish football having previously managed Villarreal, Real Madrid and Malaga.
Pellegrini who has been out of work since leaving West Ham in December. The Radio Marca report adds that former Monaco and Villarreal sporting director Antonio Cordon will be head up a new-look sporting department at the club, although this is yet to be confirmed.
Pellegrini coached Villarreal between 2004 and 2009 – famously steering them to the Champions League semi-final in 2006 – before his appointment at Real Madrid, whom he left after just one season having failed to win a trophy despite Los Blancos collecting 96 points in La Liga. He then spent three years at Malaga.
West Ham had already reached a settlement on Manuel Pellegrini’s final year on his West Ham contract meaning they will not benefit financially from him being back in work.