The screening exercise, which resumes on Tuesday, would have the former governor of Rivers State, Chibuke Amaechi take his turn alongside another nominee, Adebayo Shittu.
The nomination of Mr Amaechi has generated a lot of controversy following petitions from a group in Rivers State accusing him of fraudulent practices during his tenure as Governor of Rivers State.
Latest reports from the Nigeria Police said that the Police was still profiling the remaining nominees.
Sixteen nominees are in the second list read on the floor of the Senate by the Senate President, Dr. Bukola Saraki. Already 18 others in the first batch of nominees have been confirmed by the Senate.
The Force Public Relations Officer, Mrs Olabisi Kolawole, says screening of the second of nominees has commenced but is yet to be concluded.
She, however, gave the assurance that no ministerial nominee would be dropped by the Police.