The bill, led by MP Claire Richard, was lodged with the Vaud government on Tuesday, reported news agencies.
Manned by qualified personnel, the hotline would help combat terrorism by allowing people to voice their suspicions, feel its supporters.
“Reporting your suspicion about someone you know and asking for help is often a very difficult step to take,” say the bill's backers, feeling that a permanent hotline would help in this situation.
The canton could possibly team up with Geneva, which has already suggested a similar solution, said new agencies.
Radicalization is an increasing worry in Switzerland, as several young people have travelled to Syria to join Islamic State.
In July the Swiss government published guidelines aiming to help members of the public identify potential cases, saying they are often in a better position to detect early signs of radicalization than the security services.
The report recommended that young people, parents and teachers should be better informed about the role of the internet in radicalization, and that teachers should be given training to detect the signs of radicalization among their students.
In May the city of Winterthur, the home town of several young people who have left for Syria, opened a new service aimed at preventing radicalization.