The meeting is understood to have been the first between EchoStar chairman and chief executive Charles Ergin and Hughes since EchoStar made its move.
Ergin will outline his $27bn (£18.6bn) proposal, which would see EchoStar merge with DirecTV, its larger rival in the US satellite pay-TV market.
EchoStar's offer is believed to be less attractive than that of News Corp's, as it would likely attract a lengthy competition inquiry because a merger between DirecTV and EchoStar would create a dominant satellite pay-TV organisation.
Ergin, however, is expected to defend the deal on the grounds that the pay-TV market includes other platforms such as cable, and these should be taken into account when examining the pay-TV sector.