The 18-year old Scotland youth international is set to sign a deal with the Welsh club before being loaned back to the Jambos for the rest of the season.
Once Swansea land King, they will be bringing in a very promising player according to Scotland U19 boss Ricky Sbragia.
"Swansea have obviously seen something in Adam that's attracted them to him," Sbragia said.
"He's got that ability to learn, concentrate and focus on what's being said and then apply it in games.
"It's always a boost for a player going to a new club. The jump isn't that great at that age group, it's more about settling in and getting used to the philosophy of Swansea."
He added: "I think Adam is mature enough to deal with it.
"Whether he goes now or in the summer, I don't think Adam will go into the situation with any fear. He will just get on with it.
"Hearts have a lot of belief in him and it looks as if Swansea must have that belief as well to make the bid in the first place."
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