Alfredo - correct me if I am wrong, but your question seems to answer itself. You are proposing a parametric correlation co-efficient, presumably using either Pearson rho or Pearson product moment correlation, to test bivariate relationships - and yet you ask should it be a quantitative or qualitative approach. I personally can't see how it can relate to a qualitative approach.
I agree with Dean, Alfredo. As you have mentioned, you have and are dealing with quantitative data and are intending to apply quantitative analysis tools. Ed