Snowfall is forecast on Saturday night in parts of the Namadgi National Park and could settle Sunday morning, according to the Bureau of Meteorology.

Bureau meteorologist Neal Fraser said there wouldn't be a lot of snow.

The Bureau of Meteorology is expecting frosty mornings for the city next week. A low of minus two and top of 13 are forecast for Monday, with patches of morning frost and a slight chance of a shower.

"There's not going to be a huge amount though, because even though it's going to be very cold there's not that much moisture in the atmosphere," Mr Fraser said.

The bureau forecasts the capital to get warmer later in the week with a top of 15 degrees expected on Tuesday, 16 on Wednesday and a sunny 17 on Thursday.

The city is likely to get showers on the weekend, with rainfall forecast to begin Saturday evening and continue until Sunday morning.

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"Apart from the rainfall on Saturday afternoon and Sunday morning, it's going to be pretty dry for the rest of the time," Mr Fraser said.

The rest of the week is forecast to be frosty in the morning with temperatures tipped to rise into double digits in the day.

With just five weeks remaining until the opening of ski resorts in the Alpine regions, Perisher and Thredbo ski resorts recorded more than five centimetres of snowfall. More is expected on the weekend and early into next week.

Perisher ski resort is set to open on June 10 and early snowfall this year is looking promising for ski enthusiasts.

Perisher operations director Michael Fearnside said Perisher had 10 centimetres of snow overnight.

"A great start for the upcoming winter and it has certainly cooled the mountain down. With a follow-up fall predicted over the weekend it is a positive sign for the upcoming snow season," he said.

There are 37 days left until Thredbo Ski Resort's opening weekend and the resort is preparing for the return of live music, kids' festivals and snowboarding events.

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