London-based Brucknell, who turns 30 on Saturday, has recorded a song called “Yearning” that she hopes will win enough support through an Internet vote to put her in the running.
The Gloucestershire-born entertainer, who reached the semifinals of The X Factor in 2011, points out that Swiss regulations for the Eurovision contest allow entries from abroad, as well as Switzerland.
Chart-topping Canadian singer Céline Dion won the contest for Switzerland in 1988 without being Swiss, Brucknell noted.
"I want to bring something new and fresh to Switzerland's bid for the contest,” she said.
Brucknell said the UK hasn’t taken the competition seriously in a long time and she told The Local that she hopes by representing Switzerland with its “long history of supporting new and emerging artists” she stands a chance of competing at a "serious and credible level".
As a Swiss connection she cites that her grandfather, Robert Fisher, was educated in Switzerland before the First World War, and spoke fluent German.
The singer-songwriter, who has performed Britney Spears, Christine Aguilera and Lady Gaga tribute acts, has just released an album, Glamour and Damage, through crowd funding.
Now she is pitching for votes for her Eurovision candidacy at her www.votekitty.co.uk website.
Brucknell is competing against more than 200 other performers in an online vote that ends on Monday at 8am.
Under the Swiss selection rules, an expert jury will also weigh in with its views, with a 50 percent weighting in the vote, which will narrow the field to nine candidates.
The French-language national broadcaster RTS is selecting an additional six candidates, while Italian-language RSI is selecting another three.
The Swiss Broadcasting Corporation will reduce the number of finalists to six for a televised competition to decide who will ultimately represent Switzerland in the Eurovision contest, to be held next year in Vienna.
For a look at all the entrants vying to represent Switzerland through the Internet vote, check videos here.