The 24-year-old has had an operation to repair a damaged Achilles tendon amid fears he could be sidelined long-term with the injury.
Aluko, Hull's joint-leading scorer this season with eight goals, has been sidelined since January with a persistent Achilles problem.
But the club's medical staff are now confident he will be back in training by the middle of next month.
He has proved an instant hit with Tigers fans following his arrival in the summer from Rangers, scoring five goals in as many games in early November.
Meanwhile, fellow striker Matty Fryatt, sidelined since the Capital One Cup clash with Rotherham back in August, is making good progress following a similar operation and has targeted a return to training later this month.