Area reduction factor reference for precipitation
The answer depends on whether your data is from a single gauge or a network of gauges, and whether you have storm tracking data or not. Sounds to me like you have daily precip at a single gauge without much more information. If you know the annual average precipitation in the basin then a simple area reduction factor (ARF) calculation is basically the ratio of the annual average gauge precipitation over the basin average. 

I am not too familiar with the literature on this, but this report seems like a good starting point for background info.