"The Al Jazeera channel continues to incite violence around the Temple Mount," Netanyahu wrote in a Facebook post on Wednesday, referring to the Haram al-Sharif compound in Jerusalem, known to Jews as the Temple Mount.
"I have appealed to law enforcement agencies several times to close the Al Jazeera office in Jerusalem," said Netanyahu. "If this is not possible because of legal interpretation, I am going to seek to have the necessary legislation adopted to expel Al Jazeera from Israel."
Israel has regularly accused Al Jazeera of bias in its coverage of the Israeli-Palestinian conflict.
The network did not immediately respond to a request for comment. A spokesman for Netanyahu also did not respond to a request for further comment on the post.
Protests and deadly unrest have erupted in the days since new security measures were installed at the holy site. A tense standoff is still underway between Israel and Muslim worshippers at the Jerusalem holy site despite the removal of metal detectors and other installations there, raising concerns that the situation could deteriorate into major unrest.
The Israeli measures followed an attack that killed two policemen on July 14.
Netanyahu's remarks come as Gulf states seek Al Jazeera's closure. Regional kingpin Saudi Arabia, Bahrain, the United Arab Emirates and Egypt broke ties with Qatar on June 5, accusing it of fostering extremism and later issuing 13 demands, including Al Jazeera's closure.
Netanyahu has sought to improve ties with countries in the region, where it is heavily criticised over its 50-year occupation of Palestinian territory.
Egypt and Jordan are currently the only two Arab countries with peace treaties with Israel.
The prime minister has also faced backlash among Israelis for his decision to install the metal detectors after the attack at such an ultra-sensitive site, with many calling it a miscalculation that he was forced to back down from.
Netanyahu heads what is seen as the most right-wing government in Israeli history.
He has frequently criticised the news media, accusing it of seeking to undermine his government.