The rumours have triggered unease among investors, with Thailand's stock market sliding 2.6 per cent on Wednesday and continuing to fall on Thursday.
In recent days the army and opposition parties have escalated their attacks on Jakrapob Penkair, a minister attached to the prime minister's office accused of insulting King Bhumibol Adulyadej.
The military has strong loyalties to the palace and has in the past used alleged attacks against the monarchy as a pretext to seize power in some of Thailand's many coups.
On Thursday the English-language Bangkok Post newspaper reported that the commander of the First Army, which is based in the Thai capital, had been called back from a European trip because of the political tensions.
|Thailand has seen at least 18 coups or coup |
attempts since 1932 [GALLO/GETTY]
Selina Downes, Al Jazeera's correspondent in Bangkok, says it is difficult to assess how much popular support there would be for a coup against the government, although its position has appeared increasingly shaky in recent weeks.
Anti-government groups have said they plan to hold a major street protest for Friday.
They are demanding the resignation of the government of Samak Sundaravej, the present prime minister, for allegedly trying to amend the constitution for political gain.
The protesters accuse Samak of acting as a proxy for Thaksin Shinawatra, the former prime minister, to maintain a behind-the-scenes hold on political power.
Thailand's last coup occurred in 2006 following months of mass street protests against Thaksin's rule.
Thaksin spent more than a year in self-imposed exile following the bloodless coup but has since returned to fight the corruption charges against him and his family.
Since the end of the absolute monarchy in 1932, Thailand has seen at least 18 coups or coup attempts.