Parc Adula covers an area of 1,250km2 and affects 17 communes in total – 14 in the canton of Graubünden and three in Ticino. Some 16,000 people live there in total.
If it were granted national park status, a 142km2 core zone would be strictly protected and a further 1,108km2 would be subject to developmental constraints.
For the project to go ahead, 13 of the 17 communes that fall within the park's boundaries must approve it in this Sunday's referendum, reported news agencies on Monday.
If they do, Parc Adula will become Switzerland's second national park.
The first, called simply the Swiss National Park, was created in 1914 and covers an area of 170.3km2 in the Engadine in eastern Switzerland.
The park is subject to strict constraints in order to preserve it as a totally natural area, unaffected by human intervention.
It is only open in summer, when visitors coming to hike its 80km of trails are forbidden to camp, fish, hunt, stray off the marked paths, walk dogs or leave any mark on the landscape.
However Parc Adula's rules are likely to be less strict, federal environment minister Doris Leuthard told The Local in 2014.
Sunday's referendum is expected to be close, said news agencies.
Five of the nine communes affected by the inner strict protection zone have recommended that villagers vote yes, according to news agency ATS.
But a majority of residents are thought to be against the project, feeling that the park is unnecessary.
Farmers, hunters and alpinists in the area are particularly against it, said ATS, saying the park would place limitations on their activities.
Swiss environmental organization Pro Natura is backing the plan, saying in a 2015 statement that it was a “unique chance” to protect the natural heritage of the region in the long term.
Three more areas in Switzerland are also considered ‘candidates' for national park status.
Though Switzerland's current only national park is one of the oldest in Europe – and the first in the Alps – the country lags behind other European countries in terms of numbers, partly because of its ‘bottom up' system of governance which requires communities to approve new parks.
France has ten national parks, Germany 14 and Italy a whopping 24.