A month ago, a million people rallied in the city to support independence.
Williams said the letter would be posted later Monday on the Nobel Women's Initiative website.
Now, Spain's ruling party appears to have resorted to thinly-veiled threats in a bid to force Catalan leaders to back down as the region's independence bid threatens the breakup of Spain.
Catalonia's Parliament had been due to meet on Monday with the expectation that it would endorse the declaration of independence. "I don't think it will be better at all, because they want to take the country outside the European Union and outside of Spain".
"This situation can not be solved by violence, we have to find a solution through dialogue, this is also true when you consider the economic oint of view", he said.
"If the [Spanish] state doesn't answer positively, we will do what we came to do", he told TV3, a Catalan public channel. "This crisis needs to be resolved through dialogue at all levels of Spanish politics", France's European affairs minister Nathalie Loiseau said.
According to sources within Puidgemont's PDeCAT party, there are three possible scenarios: a full independence declaration; a "symbolic" one, with no immediate effect; or no declaration at all, and a fresh call for dialogue with Madrid.
"The exit of many companies from Catalonia is the effect of the irrational and radical policies implemented and pursued by the (regional) government", minister Luis de Guindos said as he arrived for a meeting of euro zone finance ministers in Luxembourg.
Spain's President Rajoy has said he would use all lawful means to keep Spain intact.
Spain fears the Catalan parliament could declare independence on Tuesday, when the regional government's leader is due to speak to the assembly in the wake of a banned referendum on October 1.
Mr Rajoy was quoted in a newspaper interview with German newspaper Die Welt.
On Sunday, a crowd estimated by local police to number 350,000, took to the streets of the Catalan capital Barcelona, waving Spanish and Catalan flags and carrying banners saying "Catalonia is Spain" and "Together we are stronger".
Rajoy added "we will prevent this independence from taking place".
"Credibility and dignity suggest making the declaration of independence tomorrow", said Jordi Sanchez, the head of the civil group National Catalonia Assembly said today.
Deputy Prime Minister Soraya Saenz de Santamaria told the COPE radio station Monday that "if they declare independence, there will be decisions to restore the law and democracy".
Catalans wake up on Tuesday to what could be a momentous day in their history as the world waits to see whether the region will proclaim its independence from Spain.
"I didn't feel that repressed until what happened on October 1", said 25-year-old student Mireya Jimenez.