Realizing optical analogues of quantum phenomena in atomic, molecular, or condensed matter physics has underpinned a range of photonic technologies. Rabi splitting is a quantum phenomenon induced by a strong interaction between two quantum states, and its optical analogues are of fundamental importance for the manipulation of light-matter interactions with wide applications in optoelectronics and nonlinear optics. Here, we propose and theoretically investigate purely optical analogues of Rabi splitting in integrated waveguide-coupled resonators formed by two Sagnac interferometers. By tailoring the coherent mode interference, the spectral response of the devices is engineered to achieve optical analogues of Rabi splitting with anti-crossing behavior in the resonances. Transitions between the Lorentzian, Fano, and Rabi splitting spectral lineshapes are achieved by simply changing the phase shift along the waveguide connecting the two Sagnac interferometers, revealing interesting physical insights about the evolution of different optical analogues of quantum phenomena. The impact of the device structural parameters is also analyzed to facilitate device design and optimization. These results suggest a new way for realizing optical analogues of Rabi splitting based on integrated waveguide-coupled resonators, paving the way for many potential applications that manipulate light-matter interactions in the strong coupling regime.