UN special envoy Razali Ismail, speaking on Thursday after a four-day visit to Yangon, said he believed the premier is truly committed to a transition to democracy.
"I believe he thinks there can be a working relationship established between Suu Kyi, the NLD and with him," Razali said in reference to the Nobel Peace Prize laureate's National League for Democracy.
The veteran Malaysian diplomat said Suu Kyi, whom he met twice in the villa to which she is confined, was amenable to making the process work.
"She told me she is prepared to turn a new page," he said.
Razali, who did not meet top general Than Shwe on his 12th visit to Myanmar in pursuit of national reconciliation, said Khin Nyunt needed international backing for the seven-step "road map to democracy he outlined on taking office last August to work.
"It is necessary that he be given a full mandate to take the necessary steps towards national reconciliation and democracy," he said.
Razali said Suu Kyi and the other NLD officials might be freed by April 16, Myanmar's new year, describing that date as an "informal deadline", but he did not say where it had come from.
Myanmar's military has ruled the country since 1962 and the government remains largely isolated with the United States, the European Union and Japan either imposing sanctions or withholding substantial new aid for the impoverished country.
One of their chief concerns is Suu Kyi, who was detained in May last year after a bloody clash between her supporters and government backers.
She was kept in an undisclosed location until September, when she was taken to hospital for an operation, then allowed to return to her home in Yangon.
She has remained cut off there, without a telephone and with visitors requiring government permission, saying she will not accept her liberty until all senior NLD officials are freed.