The Popular Resistance Committees (PRC) said in a statement on Saturday that the three groups had agreed to a proposal by Egyptian mediators regarding the release of corporal Gilad Shalit.
It was the first time since Shilat was captured in a cross-border raid in June that any of the factions has said that his release could happen soon.
The PRC did not give details, but said the Egyptian proposal would include the release of Palestinians held by Israel.
It added that a deal still depended on Israel. Israeli officials made no immediate comment.
Abu Mujahed, a PRC spokesman, said: "The dawn of freedom to the prisoners is about to rise and we expect a solution to our prisoners in a few days.
"We confirm to you that there is a definite move in the issue of the captured soldier."
The governing Hamas group said this week that it was optimistic about resolving the crisis, but did not set any time frame. The armed wing of Hamas is also among the groups that captured Shalit.
Hamas and its allies have demanded the release of up to 1,400 Palestinians, including minors and women, held by Israel in exchange for Shalit.
"We confirm to you that there is a definite move in the issue of the captured soldier"
The Popular Resistance Committees, Palestinian faction
Last week, Benjamin Ben-Eliezer, Israel's infrastructure minister, held talks in Cairo and afterwards expressed approval of a framework deal that Egypt had put forward, but he did not give details of the deal.
Shalit's capture prompted Israel to send troops back into the Gaza Strip almost one year after withdrawing from the territory it had captured in the 1967 war.
More than 260 Palestinians have been killed in the subsequent Israeli offensive.