The US-based Carter Centre did not confirm the meeting or "any specifics" in Carter's undisclosed itinerary.
But Sean McCormack, the state department spokesman, said the former US leader was "counselled" against meeting any Hamas representatives because it went against US foreign policy of isolating the group.
"US government policy is that Hamas is a terrorist organisation and we don't believe it is in the interests of our policy or in the interests of peace to have such a meeting," he said on Thursday.
The former president had earlier discussed with David Welch, the assistant secretary of state for Near Eastern Affairs, plans to meet Meshaal.
The centre said Carter, a Nobel Peace laureate, was leading a study mission as part of his efforts to "support peace, democracy and human rights" in the Middle East.
"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," it said in a 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."
Israel, which also calls Hamas a terrorist organisation, expressed concern over the meeting, which would be the first public contact between a US leader and Hamas officials in two years.
"The unintended consequences of such a meeting would be to embolden terrorists and undermine the cause of peace," Sallai Meridor, Israel's ambassador to the US, told Reuters.