"We're asking everybody to be ready for a crackdown," anti-government red-shirt leader Nattawut Saikua told Reuters.
Helicopters are hovering over the centre of the city, and gunfire was heard at dawn.
Thailand's government earlier rejected the protesters' offer of mediated talks.
The military made loudspeaker announcements on Wednesday morning, according to local media: "Please leave the site immediately. Officials are about to conduct an operation."
Five days of street clashes between troops and protesters in Bangkok have left 37 people dead and scores injured.
Red-shirt leaders had earlier accepted the offer of fresh talks to be overseen by senior Senate figures.
But the government said the red-shirts had to leave their Bangkok camp before any talks could take place.
Continue reading the main story Map of protest areas in Bangkok In pictures: Street fighters Bangkok clashes: The two sides have been trading increasingly bitter accusations in recent days.
The government accuses hard-liners within the red camp of using women and children as shields. At a news conference on Tuesday the military showed footage of what it said was a protester holding a baby over a barricade.
The red-shirts, meanwhile, accuse government troops of firing indiscriminately on them, although the army said troops were firing live rounds only in self-defence.
Late on Monday, the United Nations called on the protesters to "step back from the brink" and urged the government troops to exercise restraint.
Sporadic violence
On Tuesday, sporadic outbreaks of violence continued, but the BBC's South East Asia correspondent, Rachel Harvey, said that confrontations between troops and demonstrators appeared to be less intense than they once were.RED-SHIRT PROTEST
Continue reading the main story
Protests day-by-day Thai protests: Eyewitness accounts
But several thousand protesters remained inside the barricaded camp in the centre of Bangkok in continued defiance of government demands to leave.
Schools and government offices remained closed, and underground and elevated train services were suspended.
The government has extended the public holiday until Friday to allow more time to resolve the crisis - which has seen gunfire and explosions at a number of sites around the protest camp.
The red-shirts have been protesting in Bangkok since 14 March. They are currently occupying the shopping district, forcing hotels and shops to close and affecting the city's economy.
The protesters are a loose coalition of left-wing activists, democracy campaigners and mainly rural supporters of ousted leader Thaksin Shinawatra, who has lived overseas since he was convicted of conflict of interest.
They are demanding fresh polls because they say the government - which came to power through a parliamentary deal rather than an election - is illegitimate.
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