Turkish President Recep Tayyip Erdogan's push for an executive presidency succeeded with 51.4% of the electorate voting for it on Sunday.
The deputy chairman of the AKP, Mustafa Elitas, told private broadcaster NTV Monday, "It would be a great honor if he accepts it". He said that a similar procedure had been used in the past.
Sigmar Gabriel spoke on Monday in Tirana, where he was to meet with senior Albanian officials.
But "Yes" voters are singing Erdogan's praises, saying they believed Turkey's future would be safer and more prosperous with him at the helm.
The pro-Kurdish Peoples' Democratic Party (HDP), which has had two of its leaders imprisoned under President Erdogan, said the result would not be legitimate until an appeal was finalised.
However, the opposition daily Cumhuriyet's headline said "The ballot box is overshadowed", reporting opposition objections to what they said were irregularities in the voting.
Once the president's referendum victory was announced, Erdogan supporters swarmed the streets and started "hunting" down his protesters.
"Under the state of emergency put in place after the July 2016 failed coup attempt, fundamental freedoms essential to a genuinely democratic process were curtailed".
The president can also draft the state budget, a task normally carried out by parliament, and can declare a state of emergency without cabinet's approval.
About 100,000 people - including judges, teachers, academics, doctors, journalists, military officials and police - have lost their jobs in the crackdown, and more than 40,000 have been arrested. With the constitutional change, Erdogan could lead the country until 2029.
The opposition said the change would have affected the results and called for a partial recount of at least 37% of the votes, said Erdal Aksunger of the CHP.
Opposition parties called foul, complaining of a series of irregularities. "We don't know whether the amount of vote fraud was significant enough to change the outcome - or more than 1 percent - but definitely something happened".
"The Supreme Electoral Board changed rules mid-game, after the ballot envelopes were opened, in a way contrary to laws", said Kemal Kilicdaroglu, head of the main opposition People's Republican Party. Official results are due in 12 days. In the run-up to the vote, Erdogan had floated the idea of reinstating the death penalty, saying it could be taken to a referendum if need be.
"It was implemented at a moment when it was felt that the no votes were ahead of the yes votes", Tezcan said.
Merkel said Germany "respected the right of Turks to decide on their constitution" but added that "the close result shows the extent to which Turkish society is deeply divided". "Tayyip Erdogan may have done more good than the other big players (of Turkish politics) ... but I think of Tayyip Erdogan as just the best of the worst".
They fear he's already showing authoritarian tendencies.
Opponents accuse him of leading a drive towards one-man rule in Turkey, a North Atlantic Treaty Organisation member that borders Iran, Iraq and Syria and whose stability is of vital importance to the United States and European Union.
"These instructions undermined an important safeguard and contradicted the law that explicitly states that such ballots should be considered invalid", the report said.
Erdogan declared victory in the referendum on Sunday, after unofficial results showed 51.5 percent of voters had backed the constitutional changes to replace the parliamentary system with an all-powerful presidency and abolish the office of prime minister. Turkey's electoral board confirmed the "yes" victory. Guven said the decision was taken so that voters who were by mistake given unstamped ballot papers would not be "victimized".