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McCrorie is expected to be sidelined for around three weeks in a setback for the Light Blues as they prepare for Saturday night's Premiership clash at Dens Park.
There was better news regarding Sterling, who trained throughout the week after overcoming a minor hamstring concern picked up during the international break. The versatile defender also recovered from the illness that forced him off at half-time in last weekend's 3-1 win over Kilmarnock and is now in contention to start.
McInnes has also had to cope with a sickness bug affecting a number of players this week, although he does not expect it to significantly impact his selection plans.
Rangers head into the match looking to make it eight straight victories after continuing their impressive run against Neil McCann's Kilmarnock before the international break. Ryan Naderi struck twice in that victory while Kevin Kelsy also found the net.
The trip to Dundee marks the start of a busy run of fixtures for the Govan side. St Johnstone are next up at Ibrox before a midweek visit to Tynecastle to face Hearts.
A Premier Sports Cup semi-final against Aberdeen follows before the November international break brings a temporary halt to domestic action.
Aside from McCrorie's injury, McInnes has largely emerged from the international window with a clean bill of health. Cammy Devlin remains the club's main absentee after damaging his hamstring, although the Australian midfielder has avoided surgery and is expected to return in around two months.