We present the results of a real time method based on coda-wave interferometry from seismic noise cross-correlation functions for relative seismic velocity variations monitoring on a volcanic edifice. The ambient seismic noise at the Piton de la Fournaise volcano on La Réunion island is analyzed from January 2006 to June 2007. During this period, five eruptions occurred showing a great diversity in eruption duration, intensity and eruptive fissure location. Two different methods are used to compute the velocity variations in order to compare their stability in quasi real-time routine. We compare the obtained velocity variations with the surface deformation observed by GPS and extensometers networks. This allows us to identify and quantify three major processes at the origin of seismic wave velocity variations in the edifice. Firstly, the observed pre-eruptive summit inflation is accompanied by a decrease in seismic velocity. Secondly, the edifice deflation following the opening of an eruptive fissure is characterized by an increase of the velocity. Finally, the summit caldera collapse generates a strong velocity drop. Coda-wave interferometry from seismic noise cross-correlation functions in quasi-real time may allow us to forecast eruption and constrain the processes taking place in the volcanic plumbing system.