Mr Buhari, who took office at the end of May, has submitted his list of ministerial nominations, the Senate president has tweeted.
Many senators confirmed the receipt of the list but would prefer not to comment since they did not know the content of the message delivered by Senator Enang.
Saraki had on Tuesday urged the Senate to ensure that the ministerial nominees are screened quickly.
Buhari had promised at several fora that the ministerial list would be sent to the Senate on or before September 30.
The senate president however did not reply him.
Nigeria is struggling with an unprecedented economic crisis due to a plunge in oil revenues undermining the state’s ability to provide even basic services, Senate President Bukola Saraki said on Tuesday.
“If tomorrow, Thursday, were not public holiday, the list would have been announced before the Senate”, he said.
Nigeria today marks 55 years of independence, having secured its freedom from the British colonialists on October 1, 1960.
“I wish to reiterate my remarks before the Tribunal, that I have no iota of doubt that I am on trial today because I am President of the Nigerian Senate, against the wishes of a few powerful individuals outside this chambers”.
The BBC’s Will Ross in Lagos says there had been plenty of speculation that President Buhari would put himself in charge of the crucial oil ministry.
Buhari previously served as oil minister in the 1970s and head of the petroleum trust fund in the 1990s.
“The President has been under serious pressure to drop Fashola, as a topshot in the All Progressives Congress (APC) would not hear of the President appointing Fashola”.
The final decision, it was learnt, will be taken in the Presidential Villa.