Covert communication in wireless networks ensures that transmissions remain undetectable to adversaries, making it a potential enabler for privacy and security in sensitive applications. However, to meet the high performance and connectivity demands of sixth-generation (6G) networks, future wireless systems will require larger antenna arrays, higher operating frequencies, and advanced antenna architectures. This shift changes the propagation model from far-field planar-wave to near-field spherical-wave which necessitates a redesign of existing covert communication systems. Unlike far-field beamforming, which relies only on direction, near-field beamforming depends on both distance and direction, providing additional degrees of freedom for system design. In this paper, we aim to utilize those freedoms by proposing near-field Frequency Diverse Array (FDA)-based transmission strategies that manipulate the beampattern in both distance and angle, thereby establishing a non-covert region around the legitimate user. Our approach takes advantage of near-field properties and FDA technology to significantly reduce the area vulnerable to detection by adversaries while maintaining covert communication with the legitimate receiver. Numerical simulations show that our methods outperform conventional phased arrays by shrinking the non-covert region and allowing the covert region to expand as the number of antennas increases.