State Senate President Emil Jones said Burris told him about the appointment. Burris did not immediately respond to messages seeking comment.
Blagojevich was arrested earlier this month on federal charges that he tried to sell or trade the seat to the highest bidder. He has denied wrongdoing and vowed to stay in office.
In a letter signed by all 50 sitting Democratic senators, Senate Majority Leader Harry Reid of Nevada warned Blagojevich after his Dec. 9 arrest that Senate Democrats would not seat anyone the governor named to the seat.
Within minutes of the report Tuesday, Senate Democratic leaders began conferring over how to prevent Burris from actually taking office.
According to a Democratic official, who spoke on condition of anonymity because discussions were ongoing, Senate leaders were preparing a statement that would express regret for the appointment. The statement was expected to say that Senate leaders were not opposed to the former attorney general assuming the seat per se, but that under the circumstances anyone named by Blagojevich would not be seated by the Democratic caucus.
Burris became the first black politician to win statewide office when he was elected comptroller in 1978 - the first of three terms. He served one term as the state's attorney general, but he failed in three attempts at the Democratic nomination for governor, losing to Blagojevich in 2002.