The sides had earlier planned to sign the deal in late August.
"I think we'll sign it during a plenary sitting on September 10 or 11," Order and Justice Chairman Remigijus Žemaitaitis said.
"We are not stuck anywhere. Formally, it's important to do so by September 10, before the start of the session. I believe this is going to happen. In any case, there will be a cooperation agreement," Ramunas Karbauskis, chairman of the Lithuanian Farmers and Greens Union (LVŽS), said.
The Order and Justice has put forward a list of 15 measures that the Seimas should adopt by the end of its current tenure.
Žemaitaitis said that "the government has approved 12 of the 15 items".
"As to the remaining three, we'll go toward a compromise, because the government in some cases proposes a better solution", he said.
The party wants the cooperation agreement to include a commitment to raise the minimum monthly wage to at least 50 percent of the average wage, which should reach 1,000 euros next year.
Its proposals also include introducing direct elections of heads of elderships, the smallest administrative units of Lithuania, as well as the institute of jurors in courts and a reduced 9-percent tax rate for fuel used for heating.
They also call for imposing restrictions on the opening hours of major shopping centers on weekends and for increase funding for housing renovation.
The LVŽS offers the post of a Seimas vice-speaker to the Justice and Order.
The agreement would be signed by the political groups of the LVŽS, the Lithuanian Social Democratic Labor Party (LSDDP) and the Order and Justice in the parliament.
The Order and Justice has seven seats in the Seimas, the LVŽS has 55 and the LSDDP has eleven.