"I see no reason not to talk to Hamas," Brent Scowcroft, a former US national adviser to president George Bush senior, was quoted as saying.
Scowcroft signed the letter along with Zbigniew Brzezinski, another former national security adviser and Paul Volcker, Obama's economic recovery adviser, the Boston Globe said.
The letter was handed to Obama just days before he took office in January, the newspaper reported.
Mark Lynch, an associate professor of political science at George Washington University, told Al Jazeera that dealing directly with Hamas was still an "extremely controversial question" in the US.
"I think that there is a group of people who think that it is necessary. Hamas controls Gaza, you can't get aid into Gaza without working with Hamas and they represent a large portion of the Palestinian people," he said.
"On the other side you have a lot of people who say that the international community has a series of conditions. They haven't met those conditions, they have blood on their hands and there are a lot of people who have deep qualms about talking to Hamas."
Six European politicians, meanwhile, met Hamas officials, including Khaled Meshaal, the exiled political chief, in the Syrian capital, Damascus on Saturday.
"We need to talk to Hamas to make progress because they represent a big proportion of the Palestinians," Clare Short, a former minister in Britain's ruling Labour party who led the delegation, said.
Lynch said there were "significant differences" between the public positions of the US and Europe on dealing with Hamas.
"The Europeans seem, at least to my eye, more open to the possibility of working with Hamas towards meeting those conditions rather than having them as preconditions," he said.
Calls for negotiations with Hamas have grown since Israel ended its 22-day assault on the Gaza Strip in January. More than 1,300 Palestinians were killed in an operation Israel said targeted Hamas infrastructure and rocket-launching squads.
Hamas is currently engaged in talks in the Egyptian capital Cairo with the West Bank-based Fatah, which is led by Mahmoud Abbas, the Palestinian president, in an attempt to form a unity government.
However, relations between the two factions are fraught following Hamas's bloody uprising against security forces loyal to Abbas in the Gaza Strip in June 2007.
Hamas won parliamentary elections in 2006 and entered into a short-lived unity government with Fatah prior to the forcible takeover of Gaza.