Defender Mulgrew and striker Gallagher have both missed the last two games with hamstring problems, but have returned to training and will be assessed.
Midfielder Corry Evans is also nearing a return to action after a groin injury which has sidelined him since January, although the Preston match will come too soon for him.
Rovers are unbeaten in six games since Mowbray replaced Owen Coyle last month, but are only a point clear of the drop zone.
Preston boss Simon Grayson will have decisions to make on three players before naming his squad for the trip.
Alex Baptiste and Marnick Vermijl have both come through a full week of training, but may need the international break to be fully fit and ready to return to action.
Paul Gallagher, who missed last week's win over Reading, will also be monitored before the squad is selected.
John Welsh, Calum Woods and Tyias Browning remain sidelined, but are all making good progress from their respective injuries.