They said DeLay also is likely to resign his seat and leave Congress by the end of May or mid-June.
DeLay has already won the Republican primary. Rather than hold a special election for his replacement, the state central committee will probably appoint a replacement candidate, says CBSNews.com political analyst Dotty Lynch. The committee has until August to get another Republican candidate on the November ballot.
DeLay was expected to disclose his plans Tuesday at a news conference in Houston, said the officials, who spoke on the condition of anonymity because the congressman had not made that announcement.
Several officials said DeLay, an 11-term congressman, called Texas members of Congress to tell them he is dropping out of his re-election race.
"He'll resign," a former senior DeLay aide said.
In an interview with the Galveston County Daily News in Texas, DeLay said his decision was based partly on troubling internal polling results, including a poll taken after the March Republican primary that showed DeLay beating Democrat Nick Lampson in a close race.
"Even though I thought I could win, it was a little too risky," DeLay said.
DeLay stepped down from his House majority leader post in January as an election-year corruption scandal staggered Republicans and emboldened Democrats looking to reclaim power in the House and Senate.
The former exterminator was not only the majority leader but arguably the most powerful man in Congress — respected and feared and nicknamed "the hammer" for his take-no-prisoners political style, reports CBS News correspondent Bob Fuss. "He played rough and sometimes broke the rules."
DeLay was indicted by a Texas grand jury on charges related to laundering campaign funds in a Republican bid to win control of the Texas legislature in the 2002 elections.
He is accused of funneling corporate donations to Republican candidates for the Texas House in violation of state laws. A federal investigation also is pursuing DeLay's ties to disgraced lobbyist Jack Abramoff.
DeLay has denied any wrongdoing in both cases.
But DeLay's woes continued to build over the past week.
On Friday, DeLay's former chief of staff pleaded guilty to conspiracy and promised to help with a federal investigation of bribery and lobbying fraud relating to Abramoff.
Tony Rudy admitted conspiring with Abramoff — both while Rudy worked for the Texas congressman and after he left the lawmaker's staff to become a lobbyist himself.
He is the second former DeLay staffer to plead guilty to federal charges in connection with the lobbying probe. The plea agreement makes no allegation that DeLay did anything wrong.
Just days before Rudy's plea, Abramoff was sentenced to nearly six years in prison for fraud in connection with a separate case, a casino boat business deal. He was allowed to remain free while helping the congressional corruption investigation in Washington.