Szymon Hołownia, the Speaker of Poland's lower house, made the statement at a media briefing in parliament on Wednesday.
Speaking to reporters after holding talks with Morawiecki, Hołownia said that the lower house, the Sejm, "will likely appoint a new prime minister," on December 11, Polish state news agency PAP reported.
He confirmed that Morawiecki, who was reappointed prime minister earlier this week, would deliver a policy speech in parliament on the morning of December 11, followed by a floor debate and a vote of confidence at around 3 p.m.
If Morawiecki's Cabinet fails to secure a vote of confidence from MPs, the lower house will be constitutionally obliged to appoint another prime minister, Hołownia said.
The top lawmaker noted that a bloc of opposition parties had put forward Tusk as their candidate for head of government.
Hołownia told reporters that "the whole procedure," including Tusk's appointment, policy speech, and a vote of confidence in his Cabinet, could be carried out on December 11, "late into the night if necessary."
Morawiecki has led Poland’s conservative government since 2017. His new Cabinet, unveiled on Monday, includes some of his previous ministers, but also many new faces.
Poland's conservative leader Jarosław Kaczyński has said that Morawiecki's new government will work as a "team of experts" focused on "policy issues."
Polish voters elected a new set of 460 MPs and 100 senators when they went to the ballot box last month.
Morawiecki's conservative Law and Justice (PiS) party won Poland's October 15 election, but lost its parliamentary majority and looks unlikely to stay in power for a third consecutive term.
A bloc of pro-EU opposition parties in mid-November secured a resounding victory in Poland's new parliament during its first key vote to elect a house Speaker.
Poland's opposition groups have signed an agreement to form a coalition government, pledging to restore the rule of law, promote green energy and relax abortion rules, among other policies.
Opposition leader Donald Tusk, a former top EU official, has already chosen most candidates for ministerial roles in his future Cabinet, according to the Rzeczpospolita newspaper.
Hołownia told reporters last Friday that "all the names of the members of Donald Tusk's future government have been agreed on."
Tusk was Poland's prime minister from 2007 to 2014.
Source: PAP, rp.pl