There is no direct correlation between the band structure of a covalent material and the directional character of the corresponding Wannier functions. The reason is quite general. There is no direct relation between the spectrum of the eigenvalues and the spatial properties of the eigenfunctions. The only thing which is possible to establish easily is how much the band structure differs from that of a free electron gas.
However, it is enough to have a look at the band structure of a few insulators, semiconductors, $s-p$-bonded, and transition metals, to realize how difficult may be to establish a robust connection between band structure and spatial properties of wavefunctions, Wannier functions included.
If one takes into account that the characteristic signature of an insulator is the exponential decay of the Wannier functions, it should be clear that there is no chance of establishing a connection between this property of a linear combination of Bloch's states and their eigenvalues.