Blagojevich, who was arrested on Dec. 9 on corruption charges including trying to peddle the president-elect's seat for favors, scheduled a 2 p.m. CST (2000 GMT) news conference.
The governor's office would not comment on the report that he would appoint Democratic former state Attorney General Roland Burris. Burris could not be reached.
Democrat Blagojevich, 52, has denied the corruption charges and branded the impeachment effort under way in the state legislature a political lynch mob.
He has defied calls from party leaders, including Obama, that he resign. U.S. Senate Majority Leader Harry Reid wrote Blagojevich shortly after the charges were filed, warning him against making an appointment.
U.S. Senate Democratic leaders vowed on Tuesday to block any appointment by Blagojevich.
"It will ultimately not stand," the Senate Democratic leadership declared in a statement.
Illinois state election board records show Burris has made personal donations to Blagojevich's campaign organization totaling $4,500 since 2004 and his consulting firm contributed almost $11,000 since 2002.
"Roland Burris is emblematic of the old-school, pay-to-play culture that has plagued Illinois for generations and this appointment is another embarrassment for the people of Illinois," state Republican Party Chairman Andy McKenna said in a statement.
U.S. Senate Seats in Limbo
The Democrats will be in control of the U.S. Senate with at least 57 seats in the 100-seat chamber when Congress reconvenes on Jan. 6. Still in limbo are Minnesota's undecided Senate race, as well as Obama's Senate seat in Illinois.
The governor's lawyer said last week Blagojevich would refrain from making the Senate appointment.
"It's a very shrewd political move on the governor's part," said political analyst Don Rose. "The Senate has said it won't accept anybody that he proposes, but here they've come up with an African-American with very deep roots in the black community."
Burris, 71, was the first African-American elected to statewide office in Illinois in 1978 when he won the job as state Comptroller, and was the state's attorney general from 1991 to 1995.
In 1984, he lost the U.S. Senate Democratic primary to Paul Simon, and was defeated a decade later in a run for governor. He also made an unsuccessful bid to be mayor of Chicago.
He is an attorney in private practice in Chicago.
The U.S. Constitution states that the Senate decides the qualifications of its members. But if the Senate blocked the appointment, the case could likely end up in court.
In 1969, the U.S. Supreme Court ruled that the House of Representatives could not bar a member from serving, but could expel the member with a two-thirds majority vote.
