The vice president of the southern Sudan government, Riek Machar, was quoted by the official Sudan News Agency on Monday as saying the SPLM/A leadership would move to Khartoum on Wednesday.
Kiir, the agency reported, had been holding lengthy consultative meetings following the burial on Saturday of SPLM/A leader, John Garang, who died in a helicopter crash on 30 July.
Machar said Kiir would be sworn into office as Sudan's First Vice President, President of southern Sudan and successor to Garang.
He noted that there were a number of outstanding issues Garang had not settled, such as the naming of candidates to the government of national unity and to the National Assembly.
The SPLM/A, he added, also wanted to proceed with drafting the constitution for southern Sudan, and to set up the southern government and the southern legislative council.
Meanwhile Khartoum and several towns where riots broke out last week leaving more than 130 people dead, were reported calm on Monday.
At least 111 people were killed in Khartoum, while clashes in the southern towns of Juba and Malakal left 19 people dead.
The violence erupted following the announcement of Garang's death. He was en-route to southern Sudan from Uganda, following a meeting with President Yoweri Museveni, when the helicopter crashed.
Garang was buried in the southern town of Juba. Kiir, speaking at the burial which was attended by several African leaders and international delegates, appealed to all Sudanese to refrain from violence.
The Sudanese government was setting up a team to investigate the circumstances of the crash. The team would have international experts from various countries and report back as soon as possible.
Museveni on Friday said the cause of the crash was unclear and he could not rule out the possibility that it was not an accident.