Klaassen joined Premier League club Everton from Dutch giants Ajax in the summer transfer window.
According to BBC Sport, the Merseyside outfit had to pay the Eredivisie outfit a transfer fee of £23.6 million in order to secure the services of the Netherlands international attacking midfielder.
Van der Sar is also a former Ajax player, having starred for the Amsterdam outfit in the 1990s; he won the Premier League title four times and the Champions League once with Manchester United.
The former Netherlands international goalkeeper, 46, has revealed the conversation he has had with Klaassen.
“I have spoken to him and he still thinks everything in England and the Premier League is fantastic,” Van der Sar told The Mirror about Klaassen.
“But it is important that he gets plenty of minutes in the first team. Davy knows it is tough and he knows he needs to produce top-level performances to survive.”
Klaassen is a very talented and promising attacking midfielder, but the Netherlands international has not made a great start to life in the Premier League.
The 24-year-old has made three starts and one substitute appearances in the Premier League for Everton so far this season.
Everton are 14th in the Premier League table at the moment with seven points from six matches.