The club's administrators, BDO, are happy with the fee offered by Michael Laudrup's Swansea, which will net the club an immediate cash injection of £150,000.
Hearts could earn a further £50,000 through appearance-based add-ons, should the gifted 18-year-old fulfil his potential south of the border. BDO were last night locked in discussions with the Welsh side to also ensure King can see out the current season at Tynecastle, especially since losing another body would put further strain on Gary Locke's paper-thin squad.
Swansea are thought to be willing to wait until the summer before welcoming King, who is out of contract at Hearts in June, to the Liberty Stadium. Barring any unforeseen hold-ups, the player's move to Swansea - who failed in a five-figure bid for the player during the last summer transfer window - will be announced next week.
King, whose brother, Billy, is also on the books at Hearts, came through the Riccarton youth academy and has made three senior appearances for Hearts to date.