Sixty teams submitted plans for Clandon Park House in Surrey, which was reduced to a charred shell in 2015.
The National Trust has announced a shortlist of six teams, as well as the names of those on the jury, which will make a final decision after a public consultation over the summer.
Building work is expected to begin by early 2019, the National Trust said.
The National Trust said it wanted plans to combine restoring state rooms in the Grade I-listed building with new galleries and visitor spaces.
Sandy Nairne, who is chairman of the jury, said: "We received an excellent set of submissions, offering many fascinating collaborations and partnerships.
"The shortlist represents a collection of great talent from the UK and abroad.
"The teams that were selected had thoroughly analysed the conservation issues and design opportunities, and proposed thoughtful and creative approaches."
The six shortlisted teams will create concept designs which will go on public display in the late summer, The winning team is due to be announced in early autumn, the National Trust said.
The trust said the high-profile project had a Â£30m construction value.

Almost one million people have been evacuated from coastal areas in anticipation of a typhoon carrying wind speeds of 173km/h (107mph). Some 100mm of rain has fallen since Friday.
Chan-hom is now heading north past the city of Shanghai.
The typhoon hit Taiwan and Japan earlier in the week, uprooting trees and injuring several people.
Chan-hom first hit Zhejiang province on an island near the city of Ningbo at around 16:40 (08:40 GMT), the National Meteorological Center said.
No deaths or injuries were reported in the region by Saturday evening, state news agency Xinhua said.
One village, Laiao, received more than 400mm (16in) of rain, it said.
The BBC's John Sudworth in Shanghai says more than 400 flights have been cancelled there along with a number of public events, and the government has told people they should stay at home.
Dozens of flights were also cancelled in Zhoushan, Hangzhou, Ningbo and Wenzhou.
Zhejiang province has called its entire fishing fleet back to port.
Some 100 train services were also cancelled.
Peter Abram, who is in Ningbo, told the BBC: "The supermarkets got cleaned out yesterday morning. I just tried to take a walk, but got blown back inside.
"The only people out in the thick of it are emergency services... All us Westerners here in Ningbo seem to be safely battened down in our apartments, candles at the ready."
Philippa Osborne, who is in Shanghai, said: "From where I live in the middle of Shanghai, people have certainly heeded the warning to stay home. There are virtually no pedestrians out on the street, and the road traffic volume has been greatly reduced."
Chinese television showed footage of coastal regions being battered by torrential rain as the typhoon neared.
Images from the region also showed flooded farmland.
Our correspondent says China is well used to dealing with such storms, although this is possibly the strongest July typhoon to hit Zhejiang since 1949.
The highest red-alert warning remains in force, despite the storm being downgraded in category from super to strong.

The king commissioned the piano for the palace from renowned maker Thomas Tomkison in about 1821.
The instrument displays the flamboyant taste Tomkison shared with the king.
It was bought by Brighton and Hove City Council with funding from Arts Council England and the Victoria and Albert Museum,
The piano is thought to have been removed from the Pavilion by Queen Victoria after she ascended the throne in 1837.
However, its whereabouts for many years are unknown and it is thought to have held in private collections.
A Brighton Pavilion spokeswoman described the instrument as "an elegant rosewood grand, extravagantly decorated, inlaid with brass, gilt mouldings and gilt turnbuckles, with elegantly carved legs".
Councillor Alan Robins said: "King George's piano has long been on a wish list of desirable assets for the Royal Pavilion and so we're thrilled to have brought it back to its rightful home.
"The piano is playable but as it's been dormant for 20 years will need some restoration. It would be amazing to be able to hear music of the period played on it."
The National Trust has announced the design teams shortlisted to rebuild an 18th Century mansion destroyed by fire.
[NEXT_CONCEPT]
Powerful typhoon Chan-hom has made landfall along the coast of China's eastern Zhejiang province.
[NEXT_CONCEPT]
King George IV's only known surviving grand piano has been returned to Brighton's Royal Pavilion after being bought at auction for Â£62,000.