INJURY BATTLE: Jose Goncalves
In a triple bout of positive news, full-back Jason Thomson is also ready to resume training after a combination of hamstring and back injuries.
With defensive problems easing, Laszlo is anticipating a more familiar look to Hearts' back four after being forced to select the on-loan Lithuanian Marius Cinikas at right-back for the last two matches. Saturday's Scottish Cup tie at Pittodrie also brought a debut for 19-year-old Australian Rocky Visconte at left-back.
Goncalves has not featured since Hearts' 1-0 victory over Motherwell on 30 December but, after a trip to Germany, will be assessed by medical staff at Riccarton this week. Laszlo said Wallace is certain to return after missing the Aberdeen match with a heel injury.
"Lee Wallace will be no big problem, he will definitely be okay for Saturday, 100 per cent," said the Hungarian. "Jose Goncalves was in Germany and he got two or three injections and we hope this will be the cure.
"He had a scan and you can see from this that he had a small problem with his muscle. It was important not to force him to train because then you create a bigger problem. I hope he will be okay but I can't be 100 per cent sure."
Thomson last featured at first-team level in November but is close to finally rejoining his team-mates in full training. "It has been a frustrating time for Jason but hopefully he is nearing the end of this," said Laszlo. "We must be careful with him but it is positive that he is nearly ready again and we will see how he goes this week.
"I would like to have all these players back to give us more discipline and organisation because this was not always there against Aberdeen. We need to be more focused in this direction."
Meanwhile, Hearts' SPL fixture against Hamilton at Tynecastle, originally scheduled for Saturday, 20 February, has been rescheduled for Sunday, 21 February.
The match has been moved at the request of Lothian and Borders Police, who are dealing with other non-sporting events on the Saturday.