Army spokesman Sani Usman yesterday said the Chief of Army Staff, Lieutenant General Tukur Yusuf Buratai, had been told some officers and soldiers had been approached "for undisclosed political reasons".
"On the basis of that, he has warned such persons to desist from these acts," Brigadier General Usman said in an emailed statement, without elaborating.
"He also reminded them that (the) Nigerian Army is a thorough professional, disciplined, loyal and apolitical institution that has clear constitutional roles and responsibilities."
He added: "The Nigerian Army will remain apolitical and respect the Constitution of the Federal Republic of Nigeria."
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Nigeria has had six successful military coups since it gained independence from Britain in 1960, leading to decades of army rule that blighted development and fostered large- scale corruption.
The current President Muhammadu Buhari is a former army general who ousted the civilian leader in December 1983 and headed a military government for some 20 months.
Buhari, now 74 and describing himself as a "converted democrat", is currently on medical leave in London for treatment to an undisclosed condition.
No date has been set for his return, fuelling speculation about the seriousness of his illness.
Vice-President Yemi Osinbajo has been made acting president in his absence in line with the constitution.
Buratai put out a statement shortly after Buhari returned from a previous round of treatment in London in June last year and at a time of heightened tensions with oil rebels in the south.
It read: "Nobody is planning any coup.