The Leicester forward has enjoyed a great start to life at Edgar Street since moving on September 17.
Having scored on his debut, King has now helped the Bulls to two victories from his three games at the club while also chipping in with a couple of assists and man-of-the-match displays.
And the 18-year-old would like to stay with the League Two club for longer should a deal suit all parties.
He told the Bulls' official website: "I'm loving my time here, there's a great set of lads. I think we're all gelling together pretty well and I'm really enjoying it, so hopefully in due time I could maybe lengthen my stay here.
"If I keep doing well and the gaffer sees my performances getting better each week and if he's willing to give me a few more months or something like that then I'll definitely take it into consideration and help the lads out."