The ex-Formula 1 ace warned the McLaren driver that life in the public eye is affecting his form.
"Lewis is a great driver and would be an asset for any team," Coulthard told The Sun. "But he has been through the growing pains of living his life in the public eye.
"The on/off relationships, his change of management, all of this inevitably affected his form because at this level you can't just turn up and think, 'This is a Grand Prix, now I'll focus.'
"You have to focus 100% all the time."
The 27-year-old, who joined McLaren in 2007, recently expressed interest in extending his contract with the team during the upcoming Formula 1 season.