Separatist leaders have warned that such a move would fuel support for independence.
However, hundreds of thousands of people have turned out for anti-independence rallies, including in Catalonia's capital, Barcelona, since the vote.
Speaking to El Pais on Sunday, Spanish Prime Minister Mariano Rajoy said: Spain is not going to be divided and the nation's unity will be maintained.
Mr Rajoy still has not ruled out removing Catalonia's government and calling new regional elections if Puigdemont stays true to his words and claims independence.
About 10 companies have chose to relocate their legal headquarters from Catalonia to other places in Spain over fears of an unilateral declaration of independence, local media reported on Saturday.
The sides dug in as the clock ticked down to a Tuesday evening session in the regional parliament where separatists have called for an independence declaration, a plan that has raised concerns for stability in the European Union.
On Monday morning, Spain's deputy prime minister, Soraya Sáenz de Santamaría, said the government would act if Catalan government declared independence.
Tensions soared after police cracked down on voters during the banned October 1 independence referendum, prompting separatist leaders to warn they would unilaterally declare independence.
Although it is not know what Puigdemont might say, any declaration of independence from the region would likely lead to more violence.
"We have listened to many people".
IG analyst Chris Beauchamp says a positive beginning of the week for the Spanish Ibex 35 index suggests investors are confident there will be a resolution to the crisis.
A crowd estimated by local police to number 350,000 waved Spanish and Catalan flags and carried banners saying "Catalonia is Spain" and "Together we are stronger".
Careful not to undermine Rajoy, the European Union has merely called for dialogue between the sides. Rajoy assured Catalan leaders that there "is still time" to backtrack and avoid triggering a tough response from the central government in Madrid.
The Catalan president, Carles Puigdemont, is due to bring the results of the referendum before the regional parliament on Tuesday.
Catalonia, a northeastern region in Spain, has its own language and cultural traditions.
Catalan leaders say 90 percent of those who went to the polls voted to break with Spain.
Catalonia accounts for almost a fifth of Spain's economy, and leads all regions in producing 25% of the country's exports, CNNMoney reports.
Spain's government insists the independence drive is illegal and the courts ruled that the referendum breached the constitution.
The vote was not held according to official electoral standards as there were no regular voter lists, electoral commission or observers.