Last year, Lithuania temporarily reintroduced compulsory military service, planning to draft about 3,000 young men annually for five years.
President Grybauskaitė has said, however, that conscription should continue after 2020.
Last week, the president said that the State Defence Council, made up of the country's political and military leadership, would make the decision this week.
Lieutenant General Jonas Vytautas Žukas, Lithuania's chief of defence, agrees that the country should have a mixed army made up of professional serviceman and draftees.
Meanwhile Minister of National Defence Juozas Olekas has been more cautious on the issue, saying that the government and the army should first look into possibilities to man the military with professional soldiers.