Zika virus infection was declared a public health emergency of international concern in February 2016 in response to the outbreak in Brazil and its suspected link with congenital anomalies. In this study we use notification data and disease natural history parameters to estimate the basic reproduction number (R0) of Zika in Rio de Janeiro, Brazil. We also obtain estimates of R0 of dengue from time series of dengue cases in the outbreaks registered in 2002 and 2012 in the city, when DENV-3 and DENV-4 serotypes respectively, had just emerged. Our estimates of the basic reproduction number for Zika in Rio de Janeiro based on surveillance notifications (R0=2.33, 95% CI: 1.97 -- 2.97) were higher than those obtained for dengue in the city (year 2002: R0= 1.70 [1.50 -- 2.02]; year 2012: R0= 1.25 [1.18 -- 1.36]). Given the role of Aedes aegypti as vector of both the Zika and dengue viruses, we also derive R0 of Zika as a function of both dengue reproduction number and entomological and epidemiological parameters for dengue and Zika. Using the dengue outbreaks from previous years allowed us to estimate the potential R0 of Zika. Our estimates were closely in agreement with our first Zika's R0 estimation from notification data. Hence, these results validate deriving the potential risk of Zika transmission in areas with recurring dengue outbreaks. Whether transmission routes other than vector-based can sustain a Zika epidemic still deserves attention, but our results suggest that the Zika outbreak in Rio de Janeiro emerged due to population susceptibility and ubiquitous presence of Ae. aegypti.