The call came a month after Labour MP Jim Devine, whose Livingstone constituency has an agreement with the TSSA, claimed that Bennett was "presiding over a culture of fear and bullying" in a Parliamentary debate.
At the time Network Rail vehemently denied the claims and Acas voiced its confidence in Bennett.
According to news reports in the Guardian, the Commission has been brought in to investigate the matter fully.
But a spokesman from Network Rail told HR magazine: "The story in the Guardian is an another attempt by the TSSA union to stir up controversy, and I can confirm that we are in correspondence with the Equalities and Human Rights Commission.
"Network Rail has a modern, innovative and responsive HR function that takes its duty of care extremely seriously. Bullying or prejudicial behaviour is not accepted at Network Rail and where investigations into allegations reveal such behaviour Network Rail will take appropriate action against anyone, whatever their position."