The Sun says the bust-up sparked just before training at the club’s Cobham complex.
Benitez called the players into a circle to discuss Sunday’s damaging loss to Manchester City.
He expressed his dismay at the 2-0 reverse and he performance of the team and he asked the players for their reaction to the loss.
Terry, who was dropped for the game, spoke out and the discussion quickly escalated into a row between the pair.
A witness said: “It all kicked off between JT and Benitez as their frustrations over Sunday boiled over into a big bust-up.”