The seat is falling vacant following expiry of term of BJP MP Bimla Kashyap.
The Chief Electoral Officer of Himachal Pradesh said the detailed election programme would be announced soon.
The Congress Deputy leader in the Rajya Sabha is likely to be the Congress candidate for the Rajya Sabha seat, party sources said.
Sharma's term in the Rajya Sabha will end on April this year.
The Congress has a strength of 36 MLAs in the 68-member assembly. It also has the support of five Independent legislators.