Grella's long-awaited A-League debut is assured, with Aloisi certain to use the veteran at some stage as a substitute.
Babalj, released by Serbian club Red Star Belgrade back to Heart this week after the European club failed to pay his entire transfer fee, is no certainty.
The Australia striker's clearance from Red Star is not yet through, which could scuttle any hope of him featuring in the match.
Should it come through overnight as Aloisi hopes, then it will be a decision between the 20-year-old and Heart's medical and coaching staff as to how they feel he has recovered from his long flight.
"We'll ask him how he feels and have a look at him and see," Aloisi said.
"He's young, and that's always an advantage.
"When I was younger and used to go away with the national team, you could play there on a Wednesday and be back in Europe on a Saturday, and you could cope with it quite well.
"He's got that on his side."
When 33 year-old Grella takes the field, it will be a triumph of persistence and patience for both player and club.
Heart has been painstaking in its efforts to bring him back only when fully fit after a variety of niggling injuries, even outsourcing a personal training regimen for the veteran of two World Cups with the Socceroos.
Aloisi said his own late career injury problems gave him an insight into Grella's well-being and the need to be patient.
"I've had that myself towards the end of my career so I could see and feel if I was okay to play," Aloisi said.
"With Vinnie, it's the same thing. We can have a good look with the naked eye, see if he's looking good or not.
"He's worked really hard the past two months and this week he's looked as sharp as anyone out there.
"Vinnie will play a part in the game."
The Wanderers are likely to name an unchanged side from the one which beat Brisbane Roar last weekend.