Such a move would mark an unprecedented use of public property for partisan political purposes, and congressional leaders in both parties publicly doubted Trump could go ahead with the plan. Democratic House Speaker Nancy Pelosi said flatly that he "can't do that."
The president leaned into the idea during a television interview.
"I think it's a beautiful setting, and we are thinking about that," he said on Fox News Channel's "Fox & Friends." "It's certainly one of the alternatives."
He said the convention will be a mix of virtual events and live speeches, including his remarks and a speech by first lady Melania Trump. "I'll probably do mine live from the White House," he said.
The Republican National Convention is scheduled for Aug. 24-27. Trump is to be formally nominated on Aug. 24 in Charlotte, North Carolina. But the venue for his speech accepting the nomination has been up in the air.
All four days of the convention, including the speech, were planned for Charlotte until Trump feuded with the state's Democratic governor over coronavirus health restrictions. Trump then moved the speech and other elements of the convention to Jacksonville, Florida, a move welcomed by the state's Republican governor. But the president later canceled those plans because of a resurgence of the coronavirus in Florida.
That cancellation limited his options with the clock ticking.
Trump said holding the speech at the White House would be the "easiest from the standpoint of security" and the least expensive option because he - and the many staffers, Secret Service agents and others who typically accompany him - wouldn't have to travel.
Trump said a final decision hadn't been made, but he seemed to be leaning toward a White House setting for what traditionally is the highlight of a national political convention.
"If for some reason somebody had difficulty with it, I would, I could go someplace else," he said. "The easiest, least expensive and I think very beautiful would be live from the White House."
Pelosi, D-Calif., said overtly political events aren't held at the Capitol or the White House and accused Trump of trying to divert attention from his handling of the coronavirus.
"He can't do that. You can't do that," she said on MSNBC.
The No. 2 Senate Republican, John Thune of South Dakota, noted that the Hatch Act limits the ability of federal government employees to participate in partisan political activity - though Trump and Vice President Mike Pence are exempt.
"I think anything you do on federal property would seem to be problematic," Thune told reporters at the Capitol. Sen. John Cornyn, R-Texas, expressed similar concern.
"I would have to have somebody show me where it says he could do that. I would think on government property would be problematic," Cornyn said at the Capitol.
Trump also said journalists will be allowed to cover his renomination in Charlotte. Reports last week said the proceeding would be closed to media coverage because of coronavirus restrictions.
The Washington Post reported Tuesday that Republican officials were considering using the White House South Lawn to stage Trump's acceptance speech.
Presidents typically seek to hold their nominating conventions in a state seen as crucial to their chances of winning the election, but this year's coronavirus outbreak has forced candidates to change the way they campaign. Democrats are holding their convention in Wisconsin, though the event will be almost entirely virtual.
Democratic candidate Joe Biden will not travel to Milwaukee to accept his party's nomination. Delegates also are not traveling to the site, and all business, including the vote to nominate Biden, will be virtual or by mail ballot.
Presidents historically have treated the White House as a politics-free zone, though Trump has shown disregard for many norms and customs of the presidency.
Jordan Libowitz, communications director for Citizens for Responsibility and Ethics in Washington, said a separation between governing and campaigning is fundamental to democracy.
Libowitz said delivering a convention speech from the White House would follow Trump's decisions to disregard the long history of presidents and presidential candidates releasing their tax returns and to attempt to steer government business to his private for-profit properties.
"The Trump administration does not seem to care about these kinds of ethical norms for the president or really for anyone else," Libowitz said.
On Wednesday, Trump also called for the first presidential debate, scheduled for Sept. 29 in Cleveland, to be moved up because early voting will have already begun in some states. He complained that the current scheduling is "ridiculous."
The Commission on Presidential Debates, which plans the debates, had no immediate comment.
Two other presidential debates are scheduled for Oct. 15 in Miami and Oct. 22 in Nashville.
One vice presidential debate is planned for Oct. 7 in Salt Lake City.
Election Day is Nov. 3.