The reported sale has sparked an uproar among Palestinian followers of the church, who accuse the Greek leadership of betraying the Palestinian cause.
Dozens of people staged a protest in Jerusalem on Sunday, calling Patriarch Eireneos a "collaborator" and demanding his resignation.
Palestinian church leaders have also demanded that he step down.
The controversy erupted after the Israeli daily Maariv reported on Friday that the church had sold properties in the predominantly Arab sector of the walled Old City of Jerusalem.
The Old City is home to Jewish, Christian and Muslim holy sites.
A land sale to Jews in East Jerusalem, while legal, would be seen as a betrayal to Palestinians.
The Old City is home to Christian,
Muslim and Jewish holy sites
The Palestinians claim the eastern part of the city, which includes the Old City, as the site of a future capital. Israel, which captured East Jerusalem from Jordan in the 1967 war, claims the entire city.
Archbishop Aristarchos, the chief secretary of the patriarchate, declined to confirm or deny whether the sale had taken place.
"This is an unfortunate event. We are investigating," he said.
"We shall try to cancel whatever actions have been done illegally."
In a statement, the church said any sale that might have taken place was unauthorised, adding an arrest warrant had been issued in Greece for a former employee allegedly involved in the case.
During Sunday's protest, several dozen people gathered at the Church of the Holy Sepulchre - traditionally the site of Jesus Christ's crucifixion and resurrection according to Christians - and marched to the Greek Orthodox Patriarchate, chanting slogans and carrying signs such as "No to Judaization of Jerusalem" and "We will not rest until the patriarch is fired".
"This is an unfortunate event. We are investigating"
chief secretary to the Greek Orthodox Church patriarch
"What is more difficult than witnessing the sale of Jerusalem?" Ellen Kashram, a deputy school principal who joined the crowd, said.
When the patriarch left morning mass, about 10 people started heckling him and calling him a collaborator. Eireneos did not comment.
After a brief stand-off with the Israeli police, Palestinian representatives of the church who were leading the protest met privately with the patriarch's aides.
Nabil Mishahwar, chairman of the Arab Orthodox Council of Jerusalem, said church leaders denied any connection to the sale and said they suspected fraud.
The Greek Orthodox Patriarchate represents about 100,000 faithful in the Holy Land.
The church is one of the biggest property owners in Jerusalem, including large tracts of real estate inside the Old City.
It also shares control of the Church of the Holy Sepulchre with other Christian denominations.