The paper presents a method and numerical tool to daily map potential forest fire risks in geographic areas of interest, that could result particularly informative when the vegetation and terrain are highly vulnerable because of weather and fuel conditions favorable to fire outbreak. It provides information about the current fire potential ignition points, their prevalent propagation zones and the fire risks. The risks on the population and forest ecosystem services are estimated combining numerical simulations of forest fire physical behavior and dynamics with potential fire ignition points frequency, burn probability of the affected area and effective damage. The resulting maps provide information in the short term, such as daily, which are particularly useful during the night time, to support the decision makers for planning of means and resources for emergency readiness. The method implements a double Monte Carlo cycle to firstly select the potential ignition points stochastically distributed according to the statistical ignition and reignition fire frequency of the area and to secondly assess the overall risks estimating the fire propagation potential and corresponding burned area, starting from each of the identified ignition points. The method is implemented on a numerical tool for local estimations of fire risks and the paper illustrates some results of its application on a sample case in Greece.