A Te125 nuclear magnetic resonance (NMR) study was carried out in the paramagnetic state of the recently discovered quasi-one-dimensional spin-1 chain compound NiTe2O5. We observed that the Te125 NMR spectrum splits into two in a magnetic field applied along the c axis. Based on the strong temperature variation of the relative intensity ratio of the split lines, we infer that the line splitting arises from the two sublattice susceptibilities induced in opposite directions along the chains. In great support of this interpretation, a quantitative analysis of the spin-lattice relaxation rate T1−1 and the Knight shift data unravels dominant transverse spin fluctuations. We conclude that Ising-like uniaxial spin correlations persist up to surprisingly high temperatures compared to the exchange energy scales. Spin-charge coupling mechanism via a self-doping effect may be important.