However, the plan has attracted 13 letters of objection from residents and a city councillor.
The school, based at Knightswood Secondary, is the country's only fully funded centre of excellence for vocational dance and musical theatre.
It has about 80 pupils aged 11 to 17, many of whom live outside Glasgow and are housed in halls of residence at St Andrew's College, Bearsden.
However, the city council wants to provide a four-storey, purpose-built block in the grounds of Knightswood Secondary.
It would have 45 bedrooms, practice rooms, TV/social room, a dining and games hall, kitchen and space for an office, administration and storage.
A number of residents are worried the development will have an impact on the outlook from their home and result in loss of daylight.
But a report to the council's planning committee says the new accommodation will be no higher than the existing listed building on the site or the existing three-storey neighbouring tenements.
Residents also raise concern about increased noise, but council land and environmental officers have no objections to the plan.
Richard Brown, executive director of development regeneration, said a condition had been imposed on the new building restricting the use of an outdoor area to ensure residents' peace and quiet is respected. He wants the plan to get the go-ahead.
The Dance School has developed a national and international reputation and many of today's top performers in dance and musical theatre are former students.
Although the facilities, tuition and standards are regarded as outstanding, entry to the school is free."