North was knocked unconscious in the win against Wasps at the end of March and was advised to take the whole of April off before being reassessed.
He recently returned to see a specialist and the signs are good that he will be able to make a full recovery in time to play a part in his team’s Aviva Premiership title bid.
However, the 23-year-old is not expected to figure against London Welsh at Franklin’s Gardens on Saturday.
“George is improving but it’s very much in the hands of the medics as to as and when he can resume duties,” said King.
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“He went back to see the specialist and they’re happy with his progress.
“It’s very much in the hands of the medics as to when he can do more, but he’s improving and that’s all we can ask for.
“If he can play again this season it would be fantastic and if he can’t, that’s the decision.
“But at the moment he’s improving, he’s doing more and more but it’s up to the medics and they’ll be the ones who decide.”
And when it was mentioned that North has not yet been definitely ruled out for the remainder of the campaign, King said: “Until that decision’s been made, of course there’s hope.
“There are people more qualified to make these decisions than me and that’s important because we take these decisions very seriously.
“George’s health comes first and if he can play - brilliant, if he can’t then we’ll deal with it.”