The speaker, in his New Year speech on Tuesday, said the lawmakers have two options, to either stick to their guns or expunge the controversial section 87 in the bill.
He noted that the excuse of political parties not having registers is appalling and not valid.
The House resumed from the Christmas/New Year break on Tuesday.
President Muhammadu Buhari had rejected the bill, citing opposition to the controversial direct primaries clause in the bill.
Mr Buhari cited insecurity, the cost of conducting direct primaries, and infringement on the rights of Nigerians to participate in governance as his reasons for declining assent.
Opinion on the direct primary clause in the bill is divided with some saying that it should be retained while others say it should be expunged.
On Monday, the governors of the opposition Peoples Democratic Party (PDP) asked the lawmakers to either veto the president or remove the controversial areas.
Also, a former INEC Chairman, Attahiru Jega, said on Sunday that direct primaries are not feasible.
Mr Gbajabiamila said it is unlikely that the bill would be assented to by the president in its current form.
“Unfortunately, that bill did not receive presidential assent and it is unlikely that it will receive assent in its current form.
“Now we have to choose between sticking to our guns regarding the provision to mandate direct primaries for political parties or reworking that provision to save the rest of the bill.
“Let it be clear that our only objective in introducing that provision is to strengthen our democracy,” Mr Gbajabiamila said.
The Speaker also said the House will prioritise the constitution amendment bills, adding that the first draft of the passed bills will be sent to the States Houses of Assembly in February.
After the Speaker’s speech, the House went into a closed-door session.
