We present an X-ray diffuse scattering study of the pretransitional structural fluctuations of the magneto-elastic transition in alpha'-NaV2O5. This transition is characterized by the appearance below Tsp~35K of satellite reflections at the reduced wave vector (1/2,1/2,1/4). A large regime of structural fluctuations is measured up to 90 K. These fluctuations are three dimensional between Tsp and ~50K and quasi-one dimensional above ~60K. At 40 K the anisotropy ratio is found to be (xib :xia :xic)= (3.8 : 1.8 : 1), which reveals the importance of transverse interactions in the stabilization of the low temperature phase. We discuss our results within the framework of recent theories dealing with the simultaneous occurrence of a charge ordering, a spin gap and a lattice distortion in this intriguing compound.