We have carried out a multi-band photometric monitoring of the close visual binary GJ 3039 , consisting of a M4 primary and a fainter secondary component , and likely member of the young stellar association \beta Pictoris ( 24-Myr old ) . From our analysis we found that both components are photometric variables and , for the first time , we detected two micro-flare events . We measured from periodogram analysis of the photometric time series two rotation periods P = 3.355 d and P = 0.925 d , that we could attribute to the brighter GJ 3039A and the fainter GJ 3039B components , respectively . A comparison of these rotation periods with the period distribution of other \beta Pictoris members further supports that GJ 3039A is a member of this association . We find that also GJ 3039B could be a member , but the infrared magnitude differences between the two components taken from the literature and the photometric variability , which is found to be comparable in both stars , suggest that GJ 3039B could be a foreground star physically unbound to the primary A component .