The FA sent letters to City boss Mancini and Rangers counterpart Redknapp requesting their observations on their post-match comments in the wake of their sides' respective matches against Sunderland and West Brom.
Mancini and Redknapp could both find themselves charged by the FA if their words are found to have amounted to improper conduct.
Mancini hit out at referee Kevin Friend following City's 1-0 defeat at the Stadium of Light, saying: "Maybe the referee ate too much for Christmas."
The Italian was particularly angry with what he felt was a foul on Pablo Zabaleta in the build-up to Adam Johnson's winner, saying it was "impossible two men couldn't see it" in reference to Friend and his assistant.
Redknapp, meanwhile, was furious with what he claimed were two "scandalous" decisions in QPR's 2-1 home defeat to West Brom.