Their move goes against warnings that giving Myanmar's nominally civilian administration the diplomatic prize so quickly will remove the incentive for more fundamental reforms in a nation still accused of major rights abuses.
"Everybody agrees to Myanmar, 2014," Malaysian Foreign Minister Anifah Aman told reporters at Association of Southeast Asian Nations (ASEAN) talks on the Indonesian resort island of Bali.
"They have taken positive steps toward democratisation. We should encourage them more by letting them host the meeting," he said. The bloc's leaders will make a formal decision this week based on the ministers' recommendation.
In 2006, Myanmar was forced to renounce the ASEAN rotating presidency in the face of intense criticism over its human rights record and failure to shift to democracy.
But since elections a year ago that ostensibly ended decades of military rule, the new regime has unveiled surprising measures including prisoner releases that have begun to rehabilitate the nation's pariah status.
A decision to allow Myanmar to chair ASEAN would involve it hosting the 10-nation group's summit, as well as the wider East Asia Summit that includes Myanmar's arch-critic the US, which maintains sanctions against the regime.
But Myanmar's Foreign Minister Wunna Maung Lwin indicated that the decision was settled.
"All the ministers support Myanmar's chairmanship in 2014 and I welcome the decision," he told reporters.
Tan See Seng from the S. Rajaratnam School of International Studies in Singapore said the decision would be a dream come true for Myanmar's leaders who have long sought legitimacy and chafed against Western sanctions.
"Myanmar has really been putting in the right moves -- putting on a good show -- partly in regards to freeing up the political system, albeit in a very limited way," he told AFP.
"I think that for ASEAN leaders, giving Myanmar the chair would be a way of patting them on the back and encouraging them to continue what they have been recently doing domestically."
But Southeast Asian lawmakers said they were concerned that granting Myanmar the prize prematurely could end the reform process, and that it should introduce more concrete measures before being rewarded.
"This is to ensure that Myanmar will not just fool ASEAN into getting the chairmanship, and that they will continue with the democratic process," said Eva Sundari Kusuma from ASEAN's Inter-parliamentary Myanmar Caucus.
"Our call is very clear. Let us postpone. But if ASEAN agrees to let Myanmar be the chair of ASEAN, then they must put some conditionalities such as a specific action plan including the release of prisoners."
Myanmar's new administration, which is staging its diplomatic coming-out party in Bali, has surprised critics by holding direct talks with opposition leader Aung San Suu Kyi and freezing work on an unpopular mega-dam.
It freed some 200 dissidents from last month but caused disappointment by leaving many figures behind bars, and another mass release expected for Monday has been delayed for reasons that remain unclear.
There also concerns over whether President Thein Sein will follow through on the moves already made, given the risk of a backlash by hardliners who may not share his apparent enthusiasm for change.
Indonesian Foreign Minister Marty Natalegawa said ASEAN's leaders would make a formal decision on the chairmanship issue when they meet later this week.
"We discussed it thoroughly. All those who have spoken spoke in a very positive note," he said after ministerial talks Tuesday. "I would be surprised if there is any dissenting view.
"The overwhelming sense is that there are positive conditions for Myanmar's chairmanship but we hope that this chairmanship would bring more momentum for change in Myanmar."