Hastert conveyed word in a conference call one day after Republicans lost control of the House in midterm elections.
The officials who described Hastert's plans did so on condition of anonymity, saying they did not want to pre-empt a formal announcement.
His decision to step down cleared the way for a likely succession battle. Rep. John Boehner of Ohio, the majority leader, is expected to run, and Reps. Mike Pence of Indiana and Joe Barton of Texas have also signaled they may make a bid for leadership positions.
The officials said they did not know whether Hastert intended to remain in Congress. He was elected to an 11th term in Illinois on Tuesday night, and had said he would seek a new term as speaker if the GOP held the House.
There is no recent precedent for Hastert's situation. The last time control of the House changed hands, in 1994, the speaker at the time, Democratic Rep. Tom Foley of Washington, lost his House seat.
Hastert, 64, became speaker nearly eight years ago, stepping up after Newt Gingrich resigned and his heir apparent, Bob Livingston, quit after saying he had had an extramarital affair.
A former high school wrestling coach, Hastert was the perfect tonic for Republicans at the time, studiously avoiding the controversy that Gingrich often seemed to court.
He worked closely with President Bush, and originally had indicated he would retire rather than seek re-election this fall. The president prevailed on him to run again though, and Hastert agreed.
In the final weeks of the campaign, fellow Republicans questioned whether he or his aides had failed to act more quickly to force Rep. Mark Foley to resign. The Florida Republican quit Congress on Sept. 29 after being confronted with sexually explicit computer messages he had sent to teenage Capitol pages.
Hastert's tenacious — but plodding — approach to his tenure received mixed reviews. He largely shunned the talk-show circuit. Critics said he failed to line up GOP support for key legislation, including a 1999 resolution supporting U.S. intervention in Kosovo and gun-control measures.
Although conservative, Hastert became known more as a legislative tactician with a pragmatic, consensus-building style than as an ideological purist.
In an effort to keep his fragile, fractured Republican majority — and himself — in charge of the House, Hastert maintained a dizzying fundraising pace as speaker that rivaled the legendary cash-collecting abilities of his predecessor, Gingrich.
He took steps to decentralize the House, allowing policy to bubble up through the committees rather than being dictated down from the top.
Hastert won 10 terms by concentrating on issues important to his north central Illinois district, a mix of far-out Chicago suburbs, farmland and high-tech industry.
On Tuesday, Hastert was easily re-elected to his congressional seat over a relatively unknown challenger, but Democratic wins nationwide gave them control of the House and put California Democrat Nancy Pelosi in line to be the next speaker.
"It's been kind of tough out there," Hastert said during a brief appearance at his election headquarters.