King joined Rangers on loan from Scottish Premiership side Heart of Midlothian in the January transfer window.
Warburton has suggested that he is pleased with what he has seen of the 21-year-old winger so far.
The Rangers boss has also hinted that the Scottish Championship giants could try to sign the Scotland Under-21 international on a permanent contract at the end of the season.
“Billy’s a Hearts player,” Warburton told The Daily Record. “We have a loan deal that we’re delighted with and we’ll see how that progresses. He’s done really well here, every day he’s been first class.
“All the guys who have come in have really made an impression and added to the ethos and philosophy of our group. In the summer, we’ll target players who are available.”
Rangers are at the top of the Scottish Championship table at the moment with 60 points from 24 matches.
The Glasgow giants are eight points clear of second-placed Hibernian, who have a game in hand.
The Gers will take on Queen of the South away from home at Palmerston Park in the Scottish Championship on Sunday evening.
James Fowler’s side are fifth in the standings at the moment with 31 points from 22 games.