Morawiecki is seeking to secure the support of Poland's new parliament for his new-look Cabinet, Rzeczpospolita daily reported.
According to the Polish newspaper, Morawiecki's effort is destined to fail because his ruling conservative Law and Justice (PiS) party lacks a parliamentary majority.
But the governing conservatives appear to be determined to delay the handover of power at least until December 11, according to Rzeczpospolita.
Polish President Andrzej Duda this month named Morawiecki, who has led Poland's government since 2017, as prime minister-designate, tasking him with forming a new Cabinet, following last month's parliamentary election.
Under the constitution, Morawiecki has until November 27 to unveil his new government.
Meanwhile, Tusk, a former top European Union official and the leader of Poland's largest opposition bloc, the liberal Civic Coalition (KO), has already chosen most candidates for ministerial roles in his future Cabinet, according to Rzeczpospolita.
Władysław Kosiniak-Kamysz, the leader of the rural-based Polish People's Party (PSL) is set to become a deputy prime minister and defence minister; Krzysztof Gawkowski from the Left group is expected to be appointed a deputy prime minister and digitisation minister; while former ombudsman Adam Bodnar will become the new justice minister, the newspaper reported.
Meanwhile, the Civic Coalition's Radosław Sikorski is set to return to the post of foreign minister, Polish state news agency PAP reported.
Poles elected a new set of 460 MPs and 100 senators when they went to the ballot box last month.
Morawiecki's ruling 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 last week secured a resounding victory in Poland's new parliament during its first key vote to elect a house Speaker.
On November 10, Poland's pro-European opposition groups, including the Civic Coalition, PSL and the Left, 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.
Source: PAP, rp.pl