Drinkwater, 28, was a key part of Ranieri's title-winning side at Leicester which subsequently earned the midfielder a £35million to Chelsea.
While Moses has fallen down the pecking order since the exit of Antonio Conte and is seeking a move to reignite his career in England.
According to Love Sport, Ranieri's side has tabled offers for the Blues trio and an announcement is expected to be made before the end of the week.