The 21-year-old has featured 20 times for Robbie Neilson’s side this term but has been given permission by Jambos head coach Robbie Neilson to discuss a move to Ibrox.
Press Association Sport understands he travelled to Murray Park on Thursday afternoon for a medical, although the paperwork has yet to be completed.
If the deal can go through in time, King – who has 18 months left on his Tynecastle deal – will go straight into Mark Warburton’s squad to face Falkirk in Saturday’s Ladbrokes Championship clash at Ibrox.
Gers have already landed winger Harry Forrester from Doncaster for an undisclosed fee, as well as former Lech Poznan keeper Maciej Gostomski.
But there has been disappointment in the Ibrox faithful that target Toumani Diagouraga moved to Leeds despite reported interest from Gers, while the Light Blues have yet to follow up on two failed bids for St Johnstone’s Michael O’Halloran.
While not a permanent deal, the Ibrox board will hope the capture of highly-rated King – who has made over 100 appearances for Hearts and has been capped at various Scotland youth levels up to Under-21s – will appease the support as well as boosting their chances of clinching automatic promotion.
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