Andrew Bragg delivered the speech to the National Press Club on Wednesday, in which he said his party would reduce net annual migration to 180,000. That would mean a dramatic cut to international students, backpackers and unskilled workers.
Treasury modelling published in the May budget expected net overseas migration to fall from 301,000 to 225,000 by the end of this decade.
Senator Bragg freelanced on other topics outside his remit, from the NDIS to multi-national tax, before veering back to his own housing portfolio.
He declined to say whether Mr Taylor viewed the speech before it was delivered.
"I'm not going into personal interactions with colleagues. I don't think you would expect me to," he said when repeatedly pressed on the topic during an ABC Radio interview on Thursday.
"I talk widely with my colleagues."
In a blistering spray at his own party, Senator Bragg used the press club speech to say the Liberals had contributed to Australia's economic malaise and the demise of the two-party system by failing to develop enough alternative policy and wear political risk for two decades.
His colleague, James Paterson, said the speech had been a display of "personal views" rather than providing an update on the party's direction.
"We are going through our policy development process. We're doing it carefully. We're doing it deliberately," Senator Paterson told News24.
"I would just say that it's a personal view that Andrew has expressed, and that the coalition's policy will be made clear after we've gone through a deliberate, proper process," he said.
The comments came after Housing Minister Clare O'Neil slammed Senator Bragg's speech as a "crazed, almost manic ideological fever dream" when speaking to media on Wednesday.
Other coalition members, several of whom spoke to media on the condition of anonymity, also refused to back in Senator Bragg's migration proposal.
