One of the soldiers, who requested anonymity, told the BBC that at least 40 of his colleagues would refuse orders to deploy.
Wives of some soldiers recently demonstrated at the army barracks in Borno State to protest deployment of their husbands to fight the terrorists because, according to them, the Boko Haram group had better equipment than the Nigerian Army.
A state of emergency that was declared in three North Eastern states of Borno, Adamawa and Yobe last year has failed to curb the insurgency.
"Soldiers are dying like fowl," the anonymous soldier, who said he and his colleagues were just outside Maiduguri, told the BBC Hausa service.
"The Nigerian Army is not ready to fight Boko Haram," he said, explaining that soldiers were not being given enough weapons and ammunition to take them on.
"Boko Haram are inside the bush, everywhere," he said, adding that "they (senior commanders) are sacrificing soldiers".
Even the vehicles the soldiers were expected to use were old armoured cars that were not up to the job, he added.
A General in the army, who asked not to be named, told the BBC that he was unable to confirm the mutiny, but said "cowardice" was not uncommon in times of war - and that any mutineers would be punished.
When the solder was asked if he feared being court-martialled for taking part in the mutiny, the source said a soldier could only be taken to task for refusing to go to war.
"I joined the army to defend my country, but you cannot defend it without being equipped to do so", he said.
In April, Boko Haram caused global outrage by abducting more than 200 girls from the Government Girls Secondary School (GGSS), Chibok, Borno state.
Boko Haram has also carried out a wave of bombings and assassinations, including that of moderate Muslim leaders opposed to its ideology.
But the Defence Headquarters denied any mutiny by soldiers in Maiduguri.
Director of Defence Information, Chris Olukolade, a Major General, said the report of mutiny was part of calculated efforts to rubbish the military that has devoted all its powers to prosecute the war against insurgency and terrorism.
"The report is not true and even the man they spoke to is not a soldier. The Nigerian soldiers are 99 per cent loyal and would not descend to the fabrication of the report.
"Anyone who knows the military reward for mutiny will not join anyone to try it. The overwhelming majority of the Nigerian soldiers remain as brave and disciplined as ever.
"They will certainly not join any renegade, coward, deserter or those trying to incite mutiny in the military to betray the nation at a time like this in the way that impostor told his interviewers.
"His claims are false," Olukolade stated.
He argued that such reports are a reflection of those sympathetic to the terrorists, assuring that the military has the wherewithal to defeat the insurgents.
Meanwhile, Chief of Army Staff, Kenneth Minimah, a Lt. General, has warned officers and men of the 82 Division of the Nigerian Army, Enugu, that any act of mutiny would be followed with death sentence after court a martial in line with military laws.
Minimah, who was in Enugu to begin the first leg of his familiarisation visit to the division, spoke in reaction to the attack by soldiers on an army commander in the North at the peak of Boko Haram insurgency.
"We are taking charge of sabotage in the North and we are working on it. If they are found guilty that will be death by firing squad. Some may be dismissed.
"This happens more in the North and they are saboteurs against the fight against insurgenccye. I wish to announce that we have made procurement to fight the crisis in the North and I can guarantee you all that it will soon come to an end.
"I also wish to assure you that we will win this war," the Army chief said.
On the recent protest by soldiers' wives in Borno, Minimah warned that the Army will not condole that anymore, adding that they are not under the employment of army and has no role to play in its activities.
"If that repeats itself they will be kicked out of the barracks, they are meant to be controlled by their husbands. If they dare that they will see. We shall get stick and strip them naked," he added.
Source: Daily Independent