Modric has been strongly linked with a move to Premier League rivals Chelsea, who have seen offers of £22 million and £27 million rejected by Tottenham.
Spurs boss Harry Redknapp said last week that the Modric saga is now "finished", and the Croatia international made his first appearance for the club this season as Manchester City won 5-1 on Sunday.
But speculation remains over Modric's future, and King told Sky Sports News: "It's been ongoing for the whole of the summer. As players we want him to stay, he's a great lad.
"The sooner it's done, either way, the better. I don't think it (the speculation) helps at the end of the day. We've had this issue before with Berbatov. It was a similar start for us then.
"I don't think it helps in any way. As players you try and get on with the job the best you can. We, as players, want the window to close now so we can get on with the squad that we've got and get on with business."