Investors and banks are likely to help set any new timeline for public company reporting as regulators press ahead on President Donald Trump's bid to end quarterly reports, U.S. Securities and Exchange Commission Chairman Paul Atkins told CNBC Friday.

"For the sake of shareholders and public companies, the market ... can decide, you know, what the proper cadence is," Atkins said in an interview following Trump's comments earlier this week.

"Investors ... will demand that sort of information at the cadence that's appropriate to what the company's doing and what it's up to," he said, adding that banks also "will have something to say" for companies with debts, issuances and other similar issues.

Atkins did not lay out any timeline for the change, which would be a major shift for corporate America.

"In principle, I think... to propose change and what our rules are now, I think would be a good way forward, and then we'll consider that and move forward after that," he told CNBC.

Trump previously pushed the change to earnings reports in 2018 during his first White House term and renewed his call in a post on his social media platform on Monday.

Trump suggested that companies should be required to report results every six months rather than every three.

“Subject to SEC Approval, Companies and Corporations should no longer be forced to ‘Report’ on a quarterly basis (Quarterly Reporting!), but rather to Report on a ‘Six (6) Month Basis,’” Trump wrote.

• Trump Calls for End to Quarterly Reporting