King was speaking as a pundit on Sky Sports 1 immediately after Tottenham's 3-0 win at home to Manchester United.
Leicester City are currently running away with the title, seven points clear with five games left to play, and may not be able to be caught.
Spurs are chasing valiantly, with rivals Arsenal stuttering in third place.
King believes becoming North London top dogs would be worth celebrating, if it proves that first place is beyond them.
He said: "For Leicester, no one foresaw this type of season. (For Spurs) to finish above arsenal would be huge for the club."
The last time Tottenham finished above Arsenal was in 1994/95, with King never doing so in his entire career at White Hart Lane. He made his debut in 1999 before retiring due to injury problems in 2012.
He knows more than anybody what it would mean to staff and supporters if they could secure bragging rights, and make it a long summer for their North London neighbours.