There was no word if an agreement had been reached that would see the experienced coach return for what would be a third stint in charge of the side, but he has the backing of the NEC.
Bafana begin their quest for a place at the 2027 Africa Cup of Nations next month when they have qualifiers against Guinea and Eritrea. Kenya are also in their pool.
“The NEC has approved the appointment of coach Pitso to Bafana Bafana, but we still need to tie up some loose ends. We will make a formal announcement of the coach next week,” said SAFA President Danny Jordaan said.
Mosimane would take over from Broos, whose contract ended last month having taken Bafana to a first ever place in the knockout rounds at the World Cup, where they lost to Canada.
Broos, 74, was offered a new deal but has chosen to retire from active coaching.
Mosimane was first handed the reins of the national side on an interim basis in 2006 ahead of the arrival of Brazilian Carlos Alberto Parreira in the country. He was the placeholder in the dugout but took charge of some important matches.
He had seven games in charge, including a 1-0 win in Zambia in a crucial Africa Cup of Nations qualifier that remains one of Bafana’s better away victories down the years.
He had three wins and three draws to go with a single defeat, a 1-0 loss to Egypt in a friendly played in neutral London.
Mosimane then continued his role as assistant coach of the side under Parreira and Joel Santana through the 2010 World Cup, before being elevated to the top job for a second time.
He had a further 17 matches in charge, including the ill-fated bid to qualify for the 2012 Cup of Nations, where a misreading of the rules meant the side played for a draw in a game they needed to win.
His side won six of those 16 games to go with seven draws and three defeats. It was not the losses that counted against him, but the draws. Five of his last six games in charge ended level, with a 1-1 draw against Ethiopia in a 2014 World Cup qualifier the final straw.