Souttar is more likely to be fit in time as he continues recovering from an ankle problem. Halkett was due to see a specialist on Thursday to determine his chances of playing in the showpiece on May 21.
Andy Halliday and Stephen Kingsley, both forced off during last Saturday’s semi-final win against Hibs, are touch-and-go for Sunday’s league trip to Dundee United.
“Andy will be assessed on Saturday morning, as will Stephen Kingsley,” said manager Robbie Neilson. “Michael Smith is back in full training and Craig Halkett will be assessed by another specialist to see whether he will make the final or not.
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“John will start running early next week so he will be available for the final which is good news. The plan was always to try to get him back for the final couple of games of the season.
“John has big Scotland games in the summer and he wants to be part of them, as do Craig Halkett, Stephen Kingsley and Barrie McKay. They need to play well in these games and in the final to get in that squad.”
Neilson insisted he would have no issue selecting Souttar for the final despite him signing a pre-contract to join Rangers this summer.
“No, to be honest, we will pick the best team. We are hoping to have him back for the Celtic game, definitely Motherwell, which will give him a run in to the Rangers game and the final. The best players and the best team will play.”