Attorney Ed Genson said Senate leaders have already said they won't accept an appointment by Blagojevich, so there's no reason for the Democratic governor to select someone.
Blagojevich has been charged with scheming to auction the seat off to the highest bidder.
The allegation prompted calls to strip the governor of his power to choose a new senator. But Democratic lawmakers dropped that idea.
That has led to speculation about whether Blagojevich would try to make an appointment despite his legal and political problems.