Prime Minister Binali Yildirim told a meeting of the ruling Justice and Development Party (AKP) on Tuesday that the changes were needed to "eliminate confusion from the system."
"The necessary constitutional changes offered by the AKP will be offered to parliament very soon," Yildirim said.
The AKP, which currently has 317 seats in the parliament, needs a majority of 330 out of the 550 seats to call a referendum.
Chances of such a majority increased on Tuesday, when Devlet Bahceli, the leader of the Nationalist Movement Party, also known as the MHP, whose party has 40 seats, gave his strongest signal yet that he could back such a referendum.
The support by the MHP, the fourth party in the parliament by seats, would be enough to allow the referendum to go ahead even if it is opposed by the secular Republican People's Party (CHP) and the pro-Kurdish Peoples' Democratic Party (HDP).
The ruling party needs to gain 367 seats, or two-thirds of the parliament, to easily push for constitutional changes to increase the powers of the president without popular vote.
President Erdogan, who was elected in August 2014 after over 11 years of serving as prime minister, was confident before the election that he could transform Turkey into a presidential republic.
AKP officials say the constitutional changes are needed to legalize the president becoming the country's number one executive figure.
Critics say giving sweeping powers to the president could push the country into an autocracy under Erdogan.
Erdogan has also ridiculed complaints that the changes will make him a dictator, saying presidential systems exist in France and the United States.
The Turkish government has sought a presidential system more seriously since July 15, when the country crushed a coup attempt, consolidating Erdogan's power and popularity.
The coup has been followed by mass suspensions and dismissals from the public sector of people speculated to have had a role in the coup attempt.