The plan was confirmed by presidential aide Małgorzata Paprocka, Polish state PAP news agency reported.
At noon on Monday, Poland's new parliament convened for the first time.
In an interview with the PAP news agency, Paprocka said that Duda would accept the resignation of the outgoing Cabinet after the first session of the lower house.
But the president is expected to request the outgoing government ministers to continue their work until the next Cabinet is appointed, according to officials.
Duda is also expected to entrust Morawiecki with the mission of forming a new Cabinet.
Paprocka said the two would meet at the presidential palace "after the ceremonies in parliament," at around 7 or 8 p.m. on Tuesday.
Meanwhile, State Assets Minister Jacek Sasin, who is also an MP in the new parliament with the ruling conservative Law and Justice (PiS) party, told reporters on Monday that Morawiecki would seek to garner "the support of the majority of lawmakers" in the new parliament for a new government, the PAP news agency reported.
Jarosław Kaczyński, the leader of the Law and Justice party, said that Morawiecki's mission to form a new government "is not necessarily destined to fail."
He added it would be a "big achievement" if Morawiecki succeeded in his role as prime minister-designate, the PAP news agency reported.
Poles elected a new set of 460 MPs and 100 senators when they went to the ballot box last month.
Morawiecki's ruling conservatives won Poland's October 15 election, but failed to secure a parliamentary majority, increasing the likelihood of an opposition government.
Poland's pro-European opposition groups on Friday signed an agreement to form a coalition government following last month's elections, pledging to restore the rule of law, promote green energy and relax abortion rules, among other policies.
(pm/gs)
Source: PAP, rmf24.pl