We investigated an enhancement and a domain adaptation approach to make speaker verification systems robust to perturbations of far-field speech. In the enhancement approach, using paired (parallel) reverberant-clean speech, we trained a supervised Generative Adversarial Network (GAN) along with a feature mapping loss. For the domain adaptation approach, we trained a Cycle Consistent Generative Adversarial Network (CycleGAN), which maps features from far-field domain to the speaker embedding training domain. This was trained on unpaired data in an unsupervised manner. Both networks, termed Supervised Enhancement Network (SEN) and Domain Adaptation Network (DAN) respectively, were trained with multi-task objectives in (filter-bank) feature domain. On a simulated test setup, we first note the benefit of using feature mapping (FM) loss along with adversarial loss in SEN. Then, we tested both supervised and unsupervised approaches on several real noisy datasets. We observed relative improvements ranging from 2% to 31% in terms of DCF. Using three training schemes, we also establish the effectiveness of the novel DAN approach.