Burgoyne (knee) and Rioli (groin) both missed the NAB Cup opener against Richmond last week, while Lance Franklin - who has overcome a minor foot injury but will be unavailable for round one through suspension anyway - suffered a corked buttock during the game.
Burgoyne has been on a modified program since undergoing knee surgery not long after he was traded from Port Adelaide.
He took part in full training for the first time on Tuesday morning and skipper Sam Mitchell says he is hoping the 27-year-old can play some part in the pre-season before lining up for the Hawks’ first home and away game against Melbourne.
"Shaun has had a long rehab program after surgery," Mitchell said. "Our aim is to get him up and going for round one so whether he plays a half or a quarter or a full game or two full games before round one we’re not sure.
"If everything goes to plan he should be out there round one. What sort of role and nick he’s in is probably too early to tell and he has to continue to go through his program."
Franklin appeared to be in some discomfort while walking around at Waverley Park but Mitchell said there was no reason for concern.
"In the first game everyone gets a bit of a knock. It’s just a bit funny that the big superstar got one in the arse. It’s pretty funny but he trained today and kicked around alright, he’ll be fine," Mitchell said.
"We’ve got another 10 or 12 days until we have to play again so I think he will be fine by then. If he doesn’t play I don’t think it will be because of the corkie. It will be because of other reasons."
Rioli performed even lighter duties as he trained with the club’s first and second year players after the main session.
Mitchell said Rioli was recovering from minor groin problems but would be ready in time for the start of the season proper.
"I don’t think it’s OP (osteitis pubis)," Mitchell said. "The line between OP and other injuries is pretty grey. He’s got some groin soreness and tightness and it didn’t settle down straight away.
"Normally when you pick it up it goes away within one or two days. We’re being cautious with Cyril.
"If we had to play the grand final tomorrow he could play, but there is not a lot of benefit having him run around in the NAB Cup and push himself when we’ve got 26 weeks to go in the season."
