Owen was injured, along with forward Chris Annakin and captain Danny Kirmond, when the car they were travelling in hit a tree on Heath Common, near the club’s Belle Vue ground, on Friday afternoon.
Club chairman Michael Carter said: “Richie is still in hospital.
“He has had an operation on an arm, but he should be out of hospital in the next two or three days.”
Carter added: “I think Chris was in line to make his comeback [from a knee injury suffered last month] against Castleford on Friday, but it has blown that one.
“He is out of hospital and he has not had an operation as such, but he has had his hip put back into place and he’s had some work done on his ankle as well.
“There’s no prognosis at the moment how long any of them will be out of action for.
“Kirmo is out of hospital as well. He has got a deep cut to his ankle and it looks like it may have caused some damage to a tendon, but they’re not sure how severe.”
Carter is away from the club until Wednesday, but has been in touch with police investigating the accident, as well as Trinity coach Chris Chester.
“I’m liaising with the police and trying to find out exactly what happened,” he said. “By the end of the week we should have an exact idea of what went on.
“I have spoken to Chezzy and all the other boys have returned to training. Training has gone as well as can be expected. Chezzy is hopeful we’ll have two or three players back and we will have 17 players on Friday, one way or another.”