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Republican Senator Lindsey Graham says he has further questions about President Donald Trump's business dealings in relation to Russia.

The South Carolina senator asked former Director of National Intelligence James Clapper about the matter on Monday as he testified before a Senate panel.

Mr Clapper declined to answer a question about concern over any Russian ties to Mr Trump's business interests.

Mr Graham said it would be "helpful" to see President Trump's tax returns.

Russia: The scandal Trump can't shake

"I want to know more about Trump's business dealings," Mr Graham told CNN on Tuesday.

But he added it was too soon to determine whether he would be willing to subpoena them from the White House.

CNN reported that Mr Graham intended to scrutinise possible links between Mr Trump's business and Russia.

Mr Graham later clarified that the Senate judiciary committee he leads was not actively looking into Mr Trump's business relations.

"There's no effort by the judiciary committee to go after business interests because I don't know of any that are illegal or irresponsible, but if you can show me there is some evidence of that I'd be interested in it," he said.

The White House on Tuesday said it did not oppose any inquiries by Mr Graham.

White House Press Secretary Sean Spicer said the president "has no business in Russia; he has no connections to Russia."

"So he welcomes that," he added.

During Monday's testimony, Mr Clapper was asked whether he had any concerns about Mr Trump's business interests and a possible connection to Russia.

"Not in the course of the preparation of the intelligence communities assessment," said Mr Clapper, who served under former President Barack Obama.

But when Mr Graham pressed the former spy chief on whether he had ever discovered any Trump business ties to Moscow, Mr Clapper alluded to an ongoing FBI investigation.

"Senator Graham I can't comment on that because that impacts an investigation," he said.

The president took to Twitter to cast doubt on any questions surrounding Mr Clapper's refusal to comment on Monday.

"Director Clapper reiterated what everybody, including the fake media already knows- there is 'no evidence' of collusion w/ Russia and Trump,"

"The Russia-Trump collusion story is a total hoax, when will this taxpayer funded charade end?"