Coronaviruses may produce severe acute respiratory syndrome (SARS). As a matter of fact, a new SARS-type virus, SARS-CoV-2, is responsible for the global pandemic in 2020 with unprecedented sanitary and economic consequences for most countries. In the present contribution we study, by all-atom equilibrium and enhanced sampling molecular dynamics simulations, the interaction between the SARS Unique Domain and RNA guanine quadruplexes, a process involved in eluding the defensive response of the host thus favoring viral infection of human cells. Our results evidence two stable binding modes involving an interaction site spanning either the protein dimer interface or only one monomer. The free energy profile unequivocally points to the dimer mode as the thermodynamically favored one. The effect of these binding modes in stabilizing the protein dimer was also assessed, being related to its biological role in assisting the SARS viruses to bypass the host protective response. This work also constitutes a first step in the possible rational design of efficient therapeutic agents aiming at perturbing the interaction between SARS Unique Domain and guanine quadruplexes, hence enhancing the host defenses against the virus.