The General Assembly in December asked Guterres to appoint a special envoy in a resolution that called on Myanmar to end its military campaign in Rakhine state.
The appointment will be announced on Thursday, just days before the Security Council travels to Bangladesh and Myanmar for a first-hand look at the Rohingya refugee crisis.
At least 700,000 Muslim-minority Rohingya have been driven out of Myanmar and are living in crowded camps in Bangladesh since Myanmar's army launched a military operation in Rakhine state.
The violence has left a trail of torched villages in its wake, with allegations of murder and rape at the hands of troops and vigilantes.
Myanmar has vehemently denied US and United Nations allegations of ethnic cleansing. Myanmar authorities say the operation in Rakhine state is aimed at rooting out extremists.
The UN spokesman did not confirm the appointment of Schraner Burgener, but said an announcement was imminent.
Schraner Burgener has also served as Swiss ambassador to Thailand from 2009 to 2015.
She was in Zurich on Wednesday to greet German President Frank-Walter Steinmeier who is currently on a state visit to Switzerland – the first such visit by a German head of state since 2010.