The 28-year-old hopes to be declared champion in recess, which would position him to fight for his belts against whoever holds them once he is declared fit.
This increases the chances of Anthony Joshua facing Wladimir Klitschko in December for at least one of those titles. Joshua's IBF belt is also likely to be on the line in that encounter.
Speaking to BBC Radio 5Live on Sunday, Fury's uncle and trainer Peter admitted the camp are happy for his belts to be taken while he is out of action.
'The titles should be freed up, let people fight for them, Wladimir Klitschko, whoever is in line,' he said.
'Tyson should be available to fight when he comes back. Put him as a champion in recess. As soon as Tyson is ready and able, hopefully he can fight whoever has the belt and reclaim his title.
'We're boxing people and we want to see fights and world champions. Because Tyson is ill, we're happy for the belts to be freed, provided they can put him as champion in recess. As far as I'm concerned, and my team, that's what we'd be happy with.'
There is still some doubt over Fury's return to the ring though, with the British Boxing Board of Control set to meet on Wednesday to decide whether it will withdraw his licence.
In an interview with Rolling Stones magazine, Fury admitted to taking 'lots of cocaine', while claiming he was unsure if he will 'see the year out'.
Peter Fury, though, believes his nephew is getting better after seeking professional help in the last few weeks.
'I think he's okay, he's undergoing his treatment and I believe everything is going well. He's responding to the treatment and everything is looking positive.
'He's been diagnosed with some kind of manic depression. He's looking at two or three months before he can get better again.
'There's a witch hunt against him, things have spiralled out of control. The way he was received when he won the world title, to him he wasn't recognised anywhere near as much as he should have been.
'These are not good things for a young man with lots to live for. He's got a beautiful wife, lovely children, he's got everything to live for, I just don't understand it. He's got a nice house, money in the bank, I don't get it. But I'm not a doctor.
'In my opinion, I don't believe he's had drug issues going back over six months. If he's done something, I think it's been recent and I don't think he's had a drug addiction at all. I think it's a result of the depression.'
- Daily Mail and staff writer
