The Croatian midfielder has been the subject of interest from Chelsea all summer, echoing the Bulgarian striker's protracted move to Old Trafford.
Modric started in the 5-1 home defeat to Manchester City on Sunday and was frequently booed by Tottenham fans, and King feels it would be in the best interests of the club to sort out his future once and for all.
King told Sky Sports News: “To be honest it’s been going on all of the summer. It is coming into the last week now, so as players we obviously want him to stay, he’s a great lad, but the sooner it’s done, either way, the better."
The centre-back compared the situation to the 2008 summer, when Berbatov was the subject of intense interest from Manchester United before moving on the final day of the window, and feels it is a distraction.
“I don’t think it helps. We had this issue before with Berbatov a similar start to this, we didn’t start the season too well,” King added
“I don’t think it helps in any way, but as players you just try and get on and do the job the best you can.”
Modric is not the only Tottenham player being courted by other clubs at the moment, as striker Peter Crouch has attracted interest from Stoke City and Sunderland.
King said: “I don’t know what’s going to happen. We just want to get the window closed and get on with the squad we’ve got and get on with business.”