As one of the recognized ancillary services, reactive power support and voltage control plays a vital role in power system operation. Due to its importance in maintaining system security, reactive power continues to be procured by most system operators with limited financial compensation mechanisms. In this paper, the market structure for a potential reactive power market is discussed; and an auction-based reactive power market is proposed wherein the system operator is the single buyer. Furthermore, the market power held by reactive power suppliers by virtue of their strategic location in the system, is measured. The impact of reactive power market design on market power is also analyzed.