  A direct quantization of the Newtonian interaction between two masses is
known to establish entanglement, which if detected would witness the quantum
nature of the gravitational field. Gravitational interaction is yet compatible
also with gravitational decoherence models relying on classical channels, hence
unable to create entanglement. Here, we show in paradigmatic cases that,
despite the absence of entanglement, a classical-channel model of gravity can
still establish quantum correlations in the form of quantum discord between two
masses. This is demonstrated for the Kafri-Taylor-Milburn (KTM) model and a
recently proposed dissipative extension of this. In both cases, starting from
an uncorrelated state, a significant amount of discord is generally created.
This eventually decays in the KTM model, while it converges to a small
stationary value in its dissipative extension. We also find that initial local
squeezing on the state of the masses can significanlty enhance the generated
discord.
