The effect of climate change on wildfires constitutes a serious concern in fire-prone regions with complex fire behavior such as the Mediterranean. The coarse resolution of future climate projections produced by General Circulation Models (GCMs) prevents their direct use in local climate change studies. Statistical downscaling techniques bridge this gap using empirical models that link the synoptic-scale variables from GCMs to the local variables of interest (using e.g. data from meteorological stations). In this paper, we investigate the application of statistical downscaling methods in the context of wildfire research, focusing in the Canadian Fire Weather Index (FWI), one of the most popular fire danger indices. We target on the Iberian Peninsula and Greece and use historical observations of the FWI meteorological drivers (temperature, humidity, wind and precipitation) in several local stations. In particular, we analyze the performance of the analog method, which is a convenient first choice for this problem since it guarantees physical and spatial consistency of the downscaled variables, regardless of their different statistical properties. First we validate the method in perfect model conditions using ERA-Interim reanalysis data. Overall, not all variables are downscaled with the same accuracy, with the poorest results (with spatially averaged daily correlations below 0.5) obtained for wind, followed by precipitation. Consequently, those FWI components mostly relying on those parameters exhibit the poorest results. However, those deficiencies are compensated in the resulting FWI values due to the overall high performance of temperature and relative humidity. Then, we check the suitability of the method to downscale control projections (20C3M scenario) from a single GCM (the ECHAM5 model) and compute the downscaled future fire danger projections for the transient A1B scenario. In order to detect problems due to non-stationarities related to climate change, we compare the results with those obtained with a Regional Climate Model (RCM) driven by the same GCM. Although both statistical and dynamical projections exhibit a similar pattern of risk increment in the first half of the 21st century, they diverge during the second half of the century. As a conclusion, we advocate caution in the use of projections for this last period, regardless of the regionalization technique applied.