Congressman Jesse Jackson Jr. denied allegations Tuesday that he directed a businessman to offer former Illinois Gov. Rod Blagojevich millions of dollars in exchange for being appointed to the U.S. Senate seat vacated by President Barack Obama.

Jackson, who is weighing a run for Chicago mayor, has denied knowing about any offers made on his behalf ever since allegations first surfaced following Blagojevich's 2008 arrest on charges he schemed to sell or trade the Senate appointment.

This time, however, the allegations include a contention by businessman Raghuveer Nayak to the FBI that Jackson himself told Nayak, a month before Obama's election, to offer Blagojevich a total of $6 million in exchange for the Senate seat.

Jackson, a Chicago Democrat and son of civil rights leader the Rev. Jesse Jackson, issued a Tuesday statement calling Nayak's allegation "preposterous" and reiterating that while he was interested in the Senate seat, he did not engage in "some improper scheme with anyone."

Jackson also addressed Nayak's claim to the FBI that he purchased plane tickets for a woman Nayak identified as a "social acquaintance" of Jackson.

"The reference to a social acquaintance is a private and personal matter between me and my wife that was handled some time ago," Jackson said. "I ask that you respect our privacy."

His wife, Chicago Alderman Sandi Jackson, who also is considering a mayoral run, issued her own statement later Tuesday saying the issue was one her family had been "privately addressing for two years."

Nayak's allegation that Jackson told him on October 8, 2008, to make the offer to Blagojevich was first reported Tuesday by the Chicago Sun-Times. Sheldon Sorosky, one of Blagojevich's attorneys, confirmed Nayak's statements.

"Nayak told the FBI that and we received reports," Sorosky told The Associated Press. "There isn't anything in the (newspaper) report that all the lawyers in the case did not know."

Nayak's attorney, Thomas McQueen, confirmed Nayak talked to the FBI that October and said he also provided authorities with documents concerning his dealing with Jackson, but would not comment further.

Both FBI spokesman Ross Rice and U.S. Attorney's office spokesman Randy Samborn declined to comment Tuesday.

Jackson and his wife are among many people considering running for Chicago mayor after Mayor Richard Daley's surprise announcement earlier this month that he will not seek re-election to a seventh term in February. Any campaign could coincide with a second corruption trial for Blagojevich, after a jury this summer deadlocked on all but one of 24 counts against him, finding him guilty of a less serious charge of lying to the FBI.

Last week, Jackson offered a spirited denial of allegations outlined by prosecutors during Blagojevich's first trial that Jackson had attended a meeting in which Nayak offered to raise $1 million for Blagojevich's campaign in exchange for Jackson's appointment to the Senate.

In his first public comments on the issue since the trial, Jackson said on WLS Radio's "The Don Wade and Roma Show" on Friday he did meet Nayak and another businessman at a Chicago restaurant in October 2008, but never heard any discussion about a fundraising scheme. He added that he could not participate in the entire conversation because the businessmen switched to a foreign language he didn't understand.

He also challenged prosecutors.

"I assume that (prosecutors) have no evidence or they should have brought a charge," he said on the program. "If I'm a conspirator — bring it on. But I can't possibly be a conspiracy to that which I am not a part of or have no knowledge of."

Jackson subsequently did not attend a Monday jobs rally in Chicago as scheduled and his wife said he was ill. On Tuesday, Sandi Jackson's spokeswoman, Keiana Barrett, said she did not know of any immediate plans to address whether either Jackson will run for mayor.