Spurs are level on points with Chelsea following their 3-1 victory at Fulham on Sunday - but the north London side have played a game less than their London rivals, and would be just one point adrift of United providing they win their game in hand.
Deep purple: King impressed for Spurs in the win over London rivals Fulham
Tottenham haven't tasted defeat in the league since their 5-1 mauling by City at the end of August - and King, who has featured in seven games so far this campaign despite suffering from chronic knee problems, believes they can maintain their impressive form.
'I hope we can become the biggest challenger to the Manchester teams,' King said.
'We're still learning, we're still taking one game at a time, but at the moment we feel we can win every game we go into.
Hearty response: Bale celebrates after opening the scoring against Fulham
'That showed against Fulham. We didn't play well at all in the second half and we got lucky at times, our goalkeeper Brad Friedel had to pull off a few good saves for us. But when that's happening you have to dig deep and we did that.
'What they say about the old Spurs sides is that when it gets tough they weren't able to stick it out but this is a different team.
'We're managing to grind out results. That's seven wins in eight games. You have to be a good side to do that and you have to do all forms of the game. You have to defend and score goals and we're doing that.
'We're confident at the moment, we feel we've got a really good team. Everyone is maturing. We've got players that are reaching ages now when they understand the game a bit more and what's expected of them.'
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Source: Daily Mail
Source: Daily Mail