Bulger was scheduled to appear Friday before the House Committee on Government Reform, but a flurry of last-minute legal maneuvers left unclear how much Bulger will be willing to say.
For the last two years, the committee has been investigating the improper relationship between some Boston FBI agents and their mob informants.
The panel wants to question Bulger about his brother, James "Whitey" Bulger, a notorious gang leader who is wanted in connection with 21 murders. Whitey Bulger was also a top-echelon informant who provided the FBI with information about the New England faction of the Italian Mafia.
Whitey Bulger went on the run in January 1995 after being tipped off by former FBI Agent John J. Connolly Jr. that he was about to be indicted. Connolly was convicted earlier this year for warning Bulger and other mobsters about their indictments.
The committee may also question William Bulger about a real estate deal he was involved in while he was Senate president. Bulger was one of the state's most colorful and powerful politicians during 17 years as Senate president.
William Bulger lost separate bids Thursday to testify before the committee behind closed doors and to obtain copies of his earlier grand jury testimony.
Bulger's lawyer, Thomas R. Kiley, said he would ask the committee to postpone the Friday appearance.
Kiley said it is unfair that Bulger will not be given the opportunity to review his 2001 grand jury testimony.
Excerpts from his testimony were published in The Boston Globe earlier this week.
In his testimony, Bulger acknowledged he had received a phone call from his brother several weeks after he became a fugitive. He said he didn't urge his brother to surrender, "because I don't think it would be in his interest to do so."
Also Thursday, a former federal prosecutor testified he knew two mobsters were murderers and FBI informants, but did not indict them in a horse race fixing case because he felt he did not have enough evidence to convict them.
Jeremiah O'Sullivan also acknowledged that Connolly and another agent asked him not to indict James "Whitey" Bulger and Stephen "The Rifleman" Flemmi because they were informants.
But O'Sullivan said he had already made up his mind not to indict Bulger and Flemmi in the 1979 horse race fixing case, in which 21 other members and associates of the Winter Hill Gang were charged.