Not long after joining Lewis Hamilton at Mercedes this year, Finn Bottas appeared strong and he won in Russia and Austria.
But more recently, the 28-year-old has slumped.
“I experienced the same sort of difficult times when I was at McLaren with Mika (Hakkinen),” Coulthard, now a commentator for British television, told Ilta Sanomat newspaper.
“Valtteri just needs to work hard, find out where the gap to Lewis is and believe that he will be able to close it,” the Scot added.
“Valtteri is a quick and talented driver,” Coulthard continued. “As a person he is quiet and reserved, but he needs to think about his races and everything that brought him to this point and believe in himself.
“At the same time we also have to realise that he has one of the fastest ever drivers as his teammate.”