The police explained on its Facebook page that it received a petition from a senator who alleged unauthorized substitution of senate document.
It said in line with the policy of the police leadership of gathering evidence, the matter was referred to the Force CID in Abuja for investigation.
Following the investigation, a letter was subsequently sent to the clerk of the National Assembly to facilitate a meeting of some principal officers of the senate and the clerk with the police investigating team headed by the Deputy Inspector General of Police, Force CIID.
The meeting, the police said, is expected to also hold at the convenient time and location of the parties involved.
The statement said the force has respect of democratic values, and therefore has no plans to arrest the deputy senate president.
The opposition Peoples Democratic Party had on Sunday accused the ruling All Progressives Congress of petitioning of plotting the arrest of Mr. Ekweremadu after failing to force him to resign from his position.
However, following the PDP's accusation, the spokesperson for the APC, Lai Mohammed, issued a statement saying the party had no hand in Mr. Ekweremadu's ordeals.
Mr. Mohammed said the APC neither wrote a petition to the police nor is it aware that any petition was written against the deputy senate president.
Mr. Ekweremmadu is expected to appear Monday morning at the force headquarters for the questioning by the police.
At Senate plenary on June 24, Kabir Marafa (APC-Zamfara State) a senator opposed to the emergence of Bukola Saraki and Mr. Ekweremadu as President and Deputy President of the Senate respectively, made an attempt to question the June 9 elections of Messrs Saraki and Ekweremadu.
Mr. Marafa, relying on Order 110 and 3 (e) (i), of the Senate Standing Order, sought to know which of the Order Books (2011 or 2015) was used to coordinate the election.
He described the 2011 Senate Standing Order as "genuine and authentic" thereby countering the authenticity of the Senate Standing Order 2015.
The elections of Messrs. Saraki and Ekweremadu were reportedly based on a revised edition of the Senate rules, version 2015.
"I am still referring to the events of the 9th of June, 2015, in this chamber. I have two Order Books and I am running into confusion, and I think there's a need for the President to rule," Mr. Marafa said.
"Which of the Order Books are we going to use to coordinate the activities of this Senate?" he asked.
Mr. Marafa insisted that there was a conflict in the two books as to the procedure that should be taken for election of presiding officers of the senate.
He said as a former Senator, he was unaware of when the 2011 edition of the rules was amended.
Mr. Saraki however ruled Mr. Marafa out of order, thereby stopping what appears an attempt to oust him and Mr. Ekweremadu.
In his explanation that day, Mr. Ekweremadu said that from 1999 till date, the Senate had always come up with its own rules.
"There was Senate Rule of 1999, 2003, 2007, 2011 and now 2015," he said. "The reason is quite simple.
"If you look at Section 64 of the 1999 Constitution it says that the Senate and House of Representatives shall each stand dissolved at the expiration of a period of four years commencing from the date of the first sitting of the house. "So, the implication is that the rule he was referring to ended with the Senate on the 6th of June, 2015."
With the police now investigating the matter, it does appear Mr. Marafa is not prepared to allow the matter die yet.