Temir Sariev, a member of the legislature and a leader of the For Reforms opposition movement, told RFE/RL that at least 40 of Kyrgyzstan's 71 parliamentarians are in favor of holding an emergency session later today.
Sariev said the adoption of a new draft constitution would top the meeting's agenda.
It is still unclear whether the session will take place.
Thousands protesters have been picketing President Kurmanbek Bakiev's administration since November 2 to press for constitutional and other reforms.
RFE/RL's Kyrgyz Service reports the number of demonstrators reached at least 40,000 after sunset.
Their numbers swelled to well over 10,000 after Bakiev today submitted his own counterproposals to amend the existing constitution.
Turgunbek Kulmurzaev, the governor of Chui Oblast, an administrative area that includes the city of Bishkek, today joined the crowd and called upon Bakiev to resign.