Speaking to journalists in Istanbul Sunday, Cavusoglu said some surveys suggest current percentage of Yes votes to be over 58 percent, adding that more people are expected to vote Yes.
He also said the rate of voting has increased by more than 30 percent abroad compared with the previous presidential election.
"I hope there will be more. The citizens have a lot of interest," he said, adding he expects voter turnout abroad to be over 50 percent.
The overseas turnout was 8.32 percent in the 2014 presidential election, which was the first time Turkish nationals were able to vote from abroad.
Around 3 million Turkish expats are eligible to vote at Turkey’s 120 diplomatic missions in 57 countries. The overseas voting, which started Monday, will end on April 9.
Voting centers abroad remain open from 9 a.m. to 9 p.m. local time at such missions "so the citizens can also go to vote after work," Cavusoglu said.
The constitutional changes have been discussed since Recep Tayyip Erdogan was voted president in August 2014. The 18-article bill was passed by parliament in January.
The reforms would hand wide-ranging executive powers to the president and the post of prime minister would be abolished. The president would also be allowed to retain ties to a political party.
Other changes would see the minimum age for parliamentary candidates reduced to 18 and the number of deputies rise to 600.