The Spaniard finished fourth at the German Grand Prix on Sunday and currently sits 34 points behind rankings leader Sebastian Vettel.
The famous red car also trail Red Bull by 70 points in the constructors' championship, and Coulthard feels that Alonso may be forced to leave in order to find success unless Ferrari can turn their fortunes around.
"It's a long time since Alonso won a world championship and that's not because he's not putting in world championship-level performances," Coulthard told BBC Sport. "He does that all the time.
"If this continues for that much longer, you have to wonder how much longer Alonso can stay at Ferrari.
"He is 32 this year. He has still has five or so years left at the very top level, perhaps a bit more, but if Ferrari cannot get it together soon he is going to have think about his future there."
Alonso has finished first in two grands prix so far this season.