Ne Win's home is surrounded by barbed-wire barricades
No official statement has been made about the fate of Major General Myint Swe and Major General Soe Win respectively.
Burma's military authorities announced earlier that they had arrested the son-in-law and three grandsons of former strongman Ne Win on charges of plotting to overthrow the government.
Major-General Kyaw Win, the deputy chief of military intelligence, said Ne Win's son-in-law Aye Zaw Win and his children had been taken into custody on Thursday evening.
"We have arrested them for attempting to seize the state power and to split the armed forces," the general said.
Ne Win - now in his 90s - seized control of Burma in 1962 and continued to wield influence after he stepped down in 1988.
General Kyaw Win denied earlier reports that Ne Win himself and his daughter, Dandar Win, had been arrested.
Aye Zaw Win, a prominent businessman, is the daughter's husband.
He and his sons were arrested at a restaurant in the capital Rangoon where they had been discussing their plans with an unnamed former commanding officer, General Kyaw Win said.
The military intelligence officer said a number of military units and "some commanding officers" had also been involved in the plot, which was foiled in "the nick of time".
Breaking the silence
The general added that Aye Zaw Win and his sons - all in their 20s and 30s - had long enjoyed special privileges that had allowed them to build a business empire in the country that the military leadership calls Myanmar.
They had become unhappy that those favours were no longer being extended to them, the general said.
The BBC's South East Asia correspondent Jonathan Head says the explanation that the coup plans were motivated by business rivalry and not splits within the military was plausible.
It was the first acknowledgment by the government of a challenge to its power since the mass protests of 1988.
The military junta is keen to preserve unity though that has been tested by the decision to begin talks with opposition leader Aung San Suu Kyi 18 months ago, our correspondent says.
Some of the regional commanders known to be unhappy with the discussions could be implicated in the coup.
The once-powerful family of Ne Win may also be losing its influence, our correspondent adds.