We have investigated the lin∥lin CPT signal in the 87Rb D1 manifold when the atoms are contained in low pressure buffer gas cells. We predict the achievable clock frequency stability, basing our considerations on the signal-to-noise measurements. We show that a short-term stability of about 2 · 10-11 τ1/2 may be reached in a compact system using a modulated VCSEL, this value is mainly limited by the detection noise level and can be improved up to a factor 4 by using high frequency phase sensitive detection. Under the same experimental condition a challenging short-term stability of 1-3 · 10-13 τ1/2 can be achieved by using the PL ECDLs.