The Blues striker was forced to undergo surgery after sustaining the knee injury whilst playing for the Republic of Ireland against France in Paris last month and was expected to be sidelined for about five weeks.
However, Morrison is expected to begin first team training at Wast Hills at the beginning of next week and may even be in contention for a return to Steve Bruce's squad for the game against Everton at St Andrew's next Saturday evening.
The return of a forward will be a major boost to Bruce who, following Morrisons injury plus Mikael Forsell's loan deal being cut-short early because of a knee injury, has had to make do with just two recognised strikers in Emile Heskey and Dwight Yorke over the past two weeks.