it depends on the type of connectivity measure that you want to apply.
If it's DCM, then you don't need to reconstruct the activity at the sources, since the transfer function is part of the DCM itself.
Otherwise, there are several algorithms, and everyone has their favourite recipe. The two main families are the lcmv/beamformer and the loreta/wmne.
If you want to stick with matlab environment, spm, eeglab and fieldtrip have all valid source reconstruction methods.
p.s. I don't want to be a party pooper but there's no free lunch in source reconstruction connectivity. Unfortunately there's some inevitable mixing when the activity propagates to the scalp, that cannot be undone. These effects go from negligible to dramatic.