Diseases caused by the bacterium Xylella fastidiosa were recently detected in the Mediterranean Basin. The olive quick decline, caused by X. fastidiosa subsp. pauca, has devastated extensive areas in the Salento peninsula, south east Italy. An outbreak of almond leaf scorch, caused by X. fastidiosa subsp. multiplex, was detected in 2017 in Alicante province, mainland Spain. Climate is known to play an important role limiting the geographic range of Xylella diseases, but different relationships were described between X. fastidiosa and climatic covariates depending on the subsp. and the host. In this study, species distribution models were used to infer about the potential geographic distribution of olive quick decline and almond leaf scorch in the Mediterranean Basin. Data on the prevalence of X. fastidiosa in Italy and mainland Spain were gathered from official surveys. In Italy, different sampling strategies were followed each year, so the analysis was focused only in the Lecce province for the 2013-14 surveys, where a more regular sampling was observed. Monthly average climate data from 1950 to 2000 were obtained from the WorldClim database. Bayesian inference by INLA was used and the geostatistical effect was implemented by the SPDE approach. Results indicated a strong effect of the geostatistical component in the models, indicating that spatial structure has a profound impact on disease spread dynamics. Due to relatively small extent of the study areas, little variability was observed in the climate covariates and so they were not much informative in the models. Nevertheless, increasing minimum winter temperature was associated with higher probability of olive quick decline presence in Italy.