Paterson's office declined to say what the meeting would be about, but Rep. Peter King said that the governor wants to discuss possible alternate locations for the Park51 Islamic cultural center and mosque. King said he spoke with the governor Tuesday.
Representatives of the project said no meeting had been scheduled yet.
Paterson last week offered his help and the possibility that state land could be provided as an alternate site for the center.
The project has ignited nationwide debate over freedom of religion and anger over the Sept. 11 terrorist attacks.
The planned $100 million center would be built two blocks from the World Trade Center site, where nearly 2,800 people died when Islamic extremists flew jets into the twin towers. The project is headed by Imam Faisal Abdul Rauf, a Muslim cleric who has worked to improve relations between Islam and the West.
Morgan Hook, a Paterson spokesman, said talks were under way between the governor's office and representatives of Park51 to set up a meeting between Paterson and the project's leaders.
"We are working with the developers on a staff level but there have not been any formal discussions between the governor and imam or developer," Hook said. "We expect to have a meeting scheduled in the near future."
Mosque spokesman Oz Sultan released a statement Tuesday saying he did not believe a meeting had been scheduled yet.
"We appreciate the governor's interest as we continue to have conversations with many officials," Sultan said.
The Washington Post first reported the talks were under way.
King, the ranking minority leader of the Homeland Security Committee, said that he had spoken to Paterson on Tuesday and that the governor expected the meeting to take place within days.
"He said he is meeting in the next day or so with the developers and the leaders of the mosque to discuss his proposal to move it to state land. My understanding was the imam is going to be there," King told the AP.
Rauf was scheduled to leave this week on a two-week trip to the Middle East as part of a religious outreach effort by the State Department.
Meanwhile, President Barack Obama isn't worried about the furor unleashed by his comments on a planned mosque near Ground Zero, a spokesman said Tuesday.
He's also not dismayed that the Senate's top Democrat, Majority Leader Harry Reid, now opposes the idea, deputy Press Secretary Bill Burton said.
"This is an issue people are going to come to with strongly held convictions," Burton told reporters aboard Air Force One, as Obama flew to an appearance in Seattle. "He's happy our thriving democracy is continuing to produce vigorous debate."
On Monday, Reid became the highest profile Democrat to call for the mosque to be built someplace else. Current plans are to locate it two blocks from the site of the Sept. 11 terrorist attacks.
On Friday, at a White House dinner marking the Islamic holy month of Ramadan, Obama declared Muslims "have the same right to practice their religion as everyone else in this country. That includes the right to build a place of worship and a community center on private property in lower Manhattan, in accordance with local laws and ordinances."
A day later, however, Obama told reporters that wasn't an endorsement of the specifics of the mosque plan.
Burton told reporters that Obama "respects the right of anybody ... to disagree with his opinion on this."
As to Reid's view, Burton said the senator is a "fiercely independent individual," and that's one of his strengths as a leader of his fellow Democrats.
Reid is in a tough re-election fight against Republican challenger Sharron Angle, who's called the mosque plan "an affront" to the families of those who lost loved ones in the attack.
A number of Republicans have portrayed Obama as out of touch with Americans' feelings on the issue, and some Democratic strategists have said they wish he hadn't weighed in.
However, Burton said Obama didn't consider the politics of his remarks, and felt he had to speak out in defense of key constitutional values.