Earlier Thursday, Szydlo and her Cabinet easily survived a no-confidence vote in parliament called by the opposition centrist Civic Platform party, which accuses the government of harming Poland with laws that it says are anti-democratic.
The ruling Law and Justice party on Thursday picked Morawiecki, who is also deputy prime minister and development minister, to replace Prime Minister Beata Szydlo.
Government critics saw the possible leadership change as mostly a smoke screen to divert attention from a Friday vote on laws that would give the ruling party significant power over the judicial system.
Asked if, halfway through the government's term in office, the ruling party chief, Jarosław Kaczyński, would replace Beata Szydło as prime minister, Terlecki said this "will transpire around noon".
The changes in the government would need to be approved during a parliament session next week.
While Szydlo's 2-year-old government is riding high in opinion polls, Law and Justice leader Jaroslaw Kaczynski is thought to be advocating a change.
Some party members have named Finance Minister Mateusz Morawiecki, who also serves as the minister overseeing economic development, as a potential replacement for Szydlo. Poland now enjoys record low unemployment, growing wages and growth of over 4 percent per year.
Some also see Morawiecki, a former global banker who speaks foreign languages, as a better placed than Szydlo to negotiate with European partners who believe democracy is eroding in Poland.
Meanwhile, Poland's PAP news agency reported that President Andrzej Duda would be meeting with Szydło and Kaczyński on Thursday morning to discuss issues including a government reshuffle.
The meeting of the party's Political Committee was due to be followed by a gathering of the party's parliamentary caucus, PAP reported.
A Polish government official says the country's lawmakers will hold a confirmation vote next week to appoint Finance Minister Mateusz Morawiecki as the new prime minister.
The bills would give the government greater control of the judicial system and have been criticized by the European Union and others as an anti-democratic threat to Poland's rule of law.