Green, 25, was ruled out on the eve of the new Super League season having developed a blood clot in his calf.
However, a scan has now shown that the clot has disappeared, and he can now work towards returning.
Head Coach Craig Sandercock said: “Blake is responding very well to treatment and his blood clot has now resolved.
“He’ll continue with his anticoagulant therapy for the next few weeks and providing he continues to respond as he has thus far, and the haematologist gives him the all clear, we anticipate Blake will be available for approximately round 12.”
Sandercock was further boosted last week by the earlier than anticipated return of scrum half Michael Dobson from a shoulder injury.