The isoscalar monopole response has been measured in the unstable nucleus Ni68 using inelastic alpha scattering at 50A MeV in inverse kinematics with the active target MAYA at GANIL. The isoscalar giant monopole resonance (ISGMR) centroid was determined to be 21.1±1.9 MeV and indications for a soft monopole mode are provided for the first time at 12.9±1.0 MeV. Analysis of the corresponding angular distributions using distorted-wave-born approximation with random-phase approximation transition densities indicates that the L=0 multipolarity dominates the cross section for the ISGMR and significantly contributes to the low-energy mode. The L=0 part of this low-energy mode, the soft monopole mode, is dominated by neutron excitations. This demonstrates the relevance of inelastic alpha scattering in inverse kinematics in order to probe both the ISGMR and isoscalar soft modes in neutron-rich nuclei.