Rudy Giuliani told ABC’s This Week programme he had “no knowledge” of whether Michael Cohen had made other payments for the President, but said: “I would think if it was necessary, yes.”
He said Mr Cohen “made payments for the President or he’s conducted business for the President”.
Ms Daniels, whose real name is Stephanie Clifford, claims she had an affair with Mr Trump in 2006 – an allegation the President denies.
Mr Cohen paid Ms Daniels $130,000 to keep her from publicly discussing the alleged encounter – something Mr Giuliani described as a “nuisance payment”.
Mr Trump has denied he was aware of the payment, something his newly appointed lawyerRudy Giuliani has contradicted in recent days.
Mr Giuliani’s remarks on This Week come after Ms Daniels lampooned the President in a surprise appearance on Saturday Night Live.
Ms Daniels played herself in the American comedy show and warned the President that “a storm’s a-comin baby” – an appearance Mr Giuliani said was Ms Daniels trying to make “more money.”
In the sketch, Mr Trump, played by Alec Baldwin, asked his lawyer, Michael Cohen, played by Ben Stiller, to call Ms Daniels and try to fix their ongoing legal battle “once and for all”.
Mr Trump’s character sat in on the call between Mr Cohen and Ms Daniels.
He interjected and asked Ms Daniels: “What do you need for all this to just go away?”
“A resignation,” Ms Daniels said.
Mr Trump persisted, saying: “I solved North and South Korea, why can’t I solve us?”
Ms Daniels said it was too late for that.
“I know you don’t believe in climate change, but a storm’s a-comin baby,” Ms Daniels said.
The sketch also featured Kate McKinnon as Rudy Giuliani, Cecily Strong as Melania Trump, Scarlett Johansson as Ivanka Trump and Jimmy Fallon as Jared Kushner.
It is not the first time Alec Baldwin has impersonated Mr Trump on Saturday Night Live.
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A month before the 2016 presidential election, the billionaire accused the programme of a “hit job” after Baldwin compared Mr Trump to Bill Clinton in a parody sketch.
Baldwin responded by offering a truce in return for the Republican’s tax returns.