The 17-year-old put in another sparkling display as Swindon stretched their unbeaten run to eight games with a 2-1 win at Grimsby last night.
King has been delighted with the teenager's contribution since he arrived but seems resigned to losing him when the agreed month loan is up.
He said: "The boy is a terrific talent and everyone has been able to see the skills he has and I have no doubt he will go on to perform in the Premiership.
"Unfortunately he is not my player and I think when Peter Reid says a month he means a month. However that will not stop me asking the question and you never know. What I do know is the boy is enjoying his football.''
Milner himself has made no secret of his desire to figure regularly in the Leeds first team but he has no objection to staying at the County Ground for another month if that is what the two managers agree.
He said: "In terms of the immediate future, that's for Andy King and Peter Reid to talk about. The main aim is to get into the Leeds team but if the gaffer there doesn't think I'm ready then I'm more than happy to stay."
Much could depend on whether The Whites extend Jermaine Pennant's loan period at Elland Road.