The 35-year-old was placed in interim charge of the senior team three weeks ago after the club had parted company with Danny Wilson.
However, despite the fact that the team lost in the semi-final of the playoffs this afternoon to Yeovil Town, Morgan has revealed his eagerness to continue in his current position.
"There are obviously big decisions to be made," he told reporters. "I feel over the three weeks that I've had the job that I feel we've done well here, but that isn't my decision. They know I want it."
Morgan spent nine years as a player with the Blades before his retirement in 2012.