Philip Brunner and Manuel Brandberg, members of the right-wing Swiss People's Party, have proposed a motion that they hope Zug will support for a cantonal initiative seeking changes to the federal currency law.
They argue that the creation of 5,000-franc notes will ensure that the Swiss franc maintains its status as a safe haven currency.
The move goes in the opposite direction of in the European Union, where finance ministers have talked about withdrawing 500-euro bills from circulation to deter their use for financing terrorism, money laundering and other illegal activities.
But Brunner and Brandberg maintain that the tendency in the EU and in OECD member countries is to “weaken individual liberties” and to exercise greater control over citizens.
In this context “cash is comparable to the service firearm kept by Swiss citizen soldiers,” the pair argued in their motion, saying they both “guarantee freedom”.
“In France and Italy already cash payments of only up to 1,000 euros are allowed and the question of the abolition of cash is being seriously discussed and considered in Europe, “ Brunner said on his Facebook page.
The move toward electronic payments allows governments "total surveillance" over individuals, the pair claim.
Switzerland already has a 1,000-franc note (worth around $1,008), which is the most valuable banknote in Europe and second in the world only to the Singapore $10,000 note among currencies in general circulation.
Walter Meier, a spokesman for the Swiss National Bank, which is responsible for Switzerland's money, told 20 Minuten newspaper the introduction of banknotes of a higher denomination is “not an issue”.
The bank is also not planning to abolish the 1,000-franc note, which is included among the newly designed banknotes to be introduced in April.