Ahead of Saturday's Premier League clash, Tottenham are level on points with Manchester United and five points behind league leaders Manchester City.
Although Spurs were knocked out of the EFL Cup by West Ham on Wednesday, they are still in fine league form and head to Old Trafford on the back of an emphatic 4-1 victory over Liverpool.
Speaking at a Spurs Foundation's Premier League Kicks programme, King said: "Obviously there are still plenty of points to play for this season so it [the result at Old Trafford] is not going to make or break anything.
"But it is a great chance to put down a marker, to say that we are are going to be here in the run in right up to the end of the season. If we are able to go to Manchester and get a result I think everyone sits up, takes notice and knows that we're in for the race to the end.
"United are a good team but they've had some disappointing results so they'll be looking to bounce back as soon as possible. It will be a good game of football with both teams trying to win."
Harry Kane is currently the Premier League top scorer this season, and King expects the in-form striker to carry on his positive run on Saturday.
"Everyone expects him to score every week now, that's the kind of level he's reached. He's playing with such confidence he'll go into every game believing that he's going to score one or two goals."
King also compared the England striker with some of Tottenham's best ever goalscorers.
"We've obviously had legendary players like Jimmy Greaves, Jurgen Klinsmann, Teddy Sheringham. I played with Robbie Keane and Jermain Defoe. At the moment Harry's right up there with them, for sure he's one of the best strikers in the world."