Multi-block datasets are widely met in the chemometrics domain, and several data fusion approaches have recently been proposed to treat them. Apart from exploratory and predictive modelling, a key task in this context is feature selection which involves finding key complementary variables across multiple data blocks that jointly provide a good explanation of the response variables, revealing the key variables of the system. In that direction, a new method called response-oriented covariate selection (ROCS) is proposed here. ROCS is a direct extension of the covariance selection (CovSel) approach to multi-block scenarios, where the choice is based on a competition between variables in different blocks, as is done in the response-oriented sequential alternation (ROSA) method. The uniqueness of the ROCS method is its simplicity, fast execution speed, insensitivity to block order and scale-invariance. The evaluation of ROCS is presented using several multi-block modelling cases and by comparison with other variable selection methods.