He previously managed Nottingham Forest, but was let go in early September after a disagreement with owner Evangelos Marinakis.
Since his departure, Forest has appointed former Tottenham manager Ange Postecoglou, who lost his first game in charge to Arsenal on September 13.
According to reports, West Ham may offer Espirito Santo an immediate return to the Premier League, given growing concerns about the future of current manager Graham Potter.
West Ham is currently struggling, sitting in 17th place with only three points from their first four games, with their only win coming in Espirito Santo's final match as Forest manager.