Jack Butland is nearing full fitness after injuring his arm in pre-season training.
The former Rangers and England international keeper joined Hull in July 2026 for an undisclosed fee on a two-year contract, but is yet to feature in Sergej Jakirovic's side.
"He is very, very close," said the club's goalkeeping coach Erbil Bozkurt
"Before he picked up his injury, he was really supportive and helped Konstantinos Tzolakis to settle in quite well. We're looking forward to having him back, hopefully in a few weeks' time."
"I think, of course, any injury is frustrating," he added.
"The timing of Jack's one was more frustrating than anything. I think the way the injury happened, the timing of it, has not helped.
"He's a really experienced professional. He has had injuries in the past, and he knows how to overcome these things.
"You can see he is looking forward to it whenever we talk. He is really excited to be back on the grass with the team, so, hopefully, not too long."
