A whistleblower, Christopher Wylie, who worked with a Cambridge University academic to obtain the data, has alleged that the firm employed hackers to dig "dirty" information about President Muhammadu Buhari who was a candidate of the then opposition All Progressives Congress (APC).
The UK Electoral Commission is also investigating what role Cambridge Analytica played in the European Union referendum.
A presidency official, who spoke on condition of anonymity, disclosed this to PUNCH correspondents in Abuja on Sunday.
The government of Nigeria is scrutinising the reports of the data mining firm Cambridge Analytica, which swiped the data of more than 50 million Facebook users to sway elections in many countries.
Should the investigation prove that laws were broken, a special investigator could be appointed which may result in criminal prosecutions by the Attorney-General and Minister of Justice, Abubakar Malami.
The United Kingdom-based political consultancy is facing allegations that it improperly accessed data from social media website Facebook to target voters prior to United States presidential elections and Britain's Brexit referendum in 2016.
But in its reaction, the PDP accused the APC of shadow chasing but advising the ruling party to extend any probe to the Buhari 2015 campaign funds.
"The Ministry of Electronics & Information Technology, Government of India, has issued a notice.to Cambridge Analytica, wherein the serious breach of propriety and misuse of data meant to profile and influence voting behaviour has been highlighted", the IT ministry had said in a statement last month.
"It is also public knowledge that the document being relied upon by the APC clinically stated that 'there is no suggestion that Jonathan knew of the covert operation.'"We are therefore aware that this new agenda is to divert public attention from the various scandalous allegations hanging on the neck of the Buhari presidency, including the use of looted funds to finance his 2015 presidential election, the Martin Luther Kings award saga, the damaging Bill Gates verdict on the Buhari's economic policies as well as the alleged numerous financial scandals in the Nigeria National Petroleum Corporation (NNPC) under his watch".