Seasonal mean values of tropical Sea Surface Temperature (SST) and Atlantic/European Mean Sea Level Pressure (MSLP) from a 301-year coupled ocean/atmosphere model run are analysed statistically. Relations between the two fields are identified on both interannual and interdecadal timescales. It is shown that tropical SST variability affects Atlantic/European MSLP in winter. In particular, there appears to be a statistically significant relation, between the leading modes of variability, the El Niño/Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO). During cold ENSO (La Niña) years the NAO tends to be in its positive phase, while the opposite is the case during warm ENSO (El Niño) years, although to a lesser extent. Similar analyses that are presented for gridded observational data, confirm this result, although here tropical Atlantic SST appears to be stronger related to the NAO than tropical Pacific SST. The linear predictability of a model simulated NAO index is estimated by making statistical predictions that are based on model simulated tropical SST. It is shown that the predictive skill is rather insensitive to the length of the training period. On the other hand, the skill score estimate can vary significantly as a result of interdecadal variability in the climate system. These results are important to bear in mind when making statistical seasonal forecasts that are based on observed SST.