Morgan has been handed the responsibility of guiding the Blades' League One promotion bid after manager Danny Wilson and his assistant Frank Barlow parted company with the club on Thursday night.
Former Blades chief Neil Warnock is 5/1 second-favourite to make a return to the club he managed between 1999 and 2007 after leaving Leeds last week.
Paul Dickov and Paul Jewell are both available as 10/1 shots, while former United midfielder Stuart McCall, now in charge at Motherwell, is available at 12/1.
Paul Wiggins of Sky Bet said: "With the rumours of money troubles earlier in the season at Sheffield United we would be very surprised to see them go for a manager who is already in a job.
"With Chris Morgan being installed to the end of the season he seems to have the perfect chance to make the job his own if he can secure a play-off place and promotion to the Championship.
"This makes him our current 6/4 favourite to be in charge on the first day of the 2013/14 season."