The senior Hamas official in Syria told The Associated Press that Carter had sent an envoy to Damascus earlier, requesting a meeting with the militant group's officials, including exiled leader Khaled Mashaal.
Hamas "welcomed the request," said Mohammed Nazzal, who said the meeting would take place April 18.
Carter Center spokeswoman Deanna Congileo confirmed that Carter planned a trip to the Middle East at the end of the week but could not "confirm any specifics."
A press release from the center said the former Democratic president was to lead a study mission to Israel, the West Bank, Egypt, Syria, Saudi Arabia and Jordan as part of his "ongoing effort to support peace, democracy, and human rights in the region."
The statement said the visit would take place from Sunday until April 21.
"This is a study mission, and our purpose is not to negotiate, but to support and provide momentum for current efforts to secure peace in the Middle East," said Carter, according to the statement. "Our delegation has considerable experience in the region, and we go there with an open mind and heart to listen and learn from all parties."
In Washington, the State Department said it had advised Carter against meeting any representative of Hamas.
"U.S. government policy is that Hamas is a terrorist organization and we don't believe it is in the interest of our policy or in the interest of peace to have such a meeting," spokesman Sean McCormack told reporters.
He said the message had been conveyed directly to Carter in a phone call during the past week by Assistant Secretary of State for Near Eastern Affairs David Welch.
The Carter Center did not immediately respond to a request for comment.
A Carter-Mashaal meeting would be the first public contact in two years between a prominent American figure and Hamas officials. In 2006, the Rev. Jesse Jackson met Mashaal during a visit to Syria.