"We have had a long chat - I think it has to be fresh start for everybody," Jefferies told the club website.
"Things have been said and done to him but we have to get him back on track as when he first came to Hearts everyone agreed he was a real capture."
The 29-year-old last played for the Tynecastle side in mid-December and injury has restricted his appearances this season.
Kingston, who will return to training on Monday, was fined by the Edinburgh club in September for a breach of discipline and Laszlo had been upset that the player had turned out for Ghana during a period when Hearts considered him to be recovering from injury.
If I can get him battling for the cause then I'm sure the supporters will take to him again
"The aim is to get him back with his head right and get him back competing and giving full value," said Jefferies, whose side next play on Wednesday against Celtic in Glasgow.
"It has to be a two-way thing, though - it's not just me who wants that, he has to want it, too. If you are going to work together, you work together as a partnership."
"The fans took to him when he arrived and all I can do is work with him and instil a belief in him that if he wants to perform and play for the club as he did when he first came, the supporters will be delighted.
"It was nice to hear him say: 'I'll play wherever you want me to gaffer, right, left wherever'.
"I always heard he wasn't happy when picked to play in certain positions but he said that wasn't the case so I'm going to hold him to that.
"He's a creative player with plenty of skill and we need that in the team. But I also need him working hard and if I can get him battling for the cause then I'm sure the supporters will take to him again."
Source: BBC Sport