Negative feedback from active galactic nuclei (AGN) is considered a key mechanism in shaping galaxy evolution. Fast, extended outflows are frequently detected in the AGN host galaxies at all redshifts and luminosities, both in ionised and molecular gas. However, these outflows are only potentially able to quench star formation, and we are still lacking decisive evidence of negative feedback in action. Here we present observations obtained with the Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI) H- and K-band integral-field of two quasars at z ∼ 2.4 that are characterised by fast, extended outflows detected through the [Oiii]λ5007 line. The high signal-to-noise ratio of our observations allows us to identify faint narrow (FWHM< 500 km s-1) and spatially extended components in [Oiii]λ5007 and Hα emission associated with star formation in the host galaxy. This star formation powered emission is spatially anti-correlated with the fast outflows. The ionised outflows therefore appear to be able to suppress star formation in the region where the outflow is expanding. However, the detection of narrow spatially extended Hα emission indicates star formation rates of at least ∼50-90 M⊙ yr-1, suggesting either that AGN feedback does not affect the whole galaxy or that many feedback episodes are required before star formation is completely quenched. On the other hand, the narrow Hα emission extending along the edges of the outflow cone may also lead also to a positive feedback interpretation. Our results highlight the possible double role of galaxy-wide outflows in host galaxy evolution.