Kjellander denied he had ever discussed such a thing and Rove's lawyer, Robert Luskin, said his client had no memory of such discussions.
Maloof's testimony Monday was the first time Hastert's name had come up in testimony.
"The conversation was that Mr. Hastert would name a new U.S. attorney," Maloof said.
"What would be the effect of having a new U.S. attorney on the investigation?" Assistant U.S. Attorney Christopher Niewoehner asked.
"They would order the prosecutor to drop the investigation," said Maloof, who was not asked to elaborate on who "they" were.
Republicans in Washington could presumably be persuaded to spike an investigation into Democrat Blagojevich because Rezko raised money for the GOP too and is accused of scheming with Republican heavyweight Stuart Levine, who has pleaded guilty in the case and testified against Rezko.
Kjellander, former treasurer of the Republican National Committee, received $809,000 in consulting fees for Blagojevich's 2003 sale of state bonds, much of which prosecutors believe was funneled through a Rezko associate to Rezko "assignees." Kjellander has not been charged with wrongdoing.
Rezko, 52, is charged with scheming to split a $1.5 million bribe from a contractor who wanted state permission to build a hospital in the McHenry County suburb of Crystal Lake and pressure kickbacks out of money management firms seeking to do business with a state pension fund.
Prosecutors say Rezko's fundraising for Blagojevich made him highly influential in the administration and as a result he could manipulate the state boards that decide on hospital construction and allocate money from the pension fund to investment firms.
U.S. attorneys are nominated by the president but traditionally are chosen by the senior senator of the president's party.
Fitzgerald was the candidate of Sen. Peter Fitzgerald, R-Ill., no relation, who said openly that he wanted someone from out of state who would be independent and attack the corruption long plaguing Illinois.
Since taking over as U.S. attorney in September 2001, Patrick Fitzgerald has launched a vigorous attack on corruption, sending former Gov. George Ryan and a number of other political insiders to federal prison.
Peter Fitzgerald and Hastert, while both Republicans, often were at odds with each other. It would not be unusual to allow a senior congressman to suggest a candidate for U.S. attorney if there were no senator of the president's party from the state.
Maloof, a former employee of a Rezko pizza business, testified under a grant of immunity from prosecution for anything he might say on the stand.
Among other things, he testified that Rezko told him to say as little as possible when called before a federal grand jury investigating corruption in the Blagojevich administration.
And he said Rezko told him anything he might say about Rezko himself would "tie back to Blagojevich."
The governor has not been charged with any wrongdoing in the case.
The Associated Press contributed to this report.