The 23-year-old has made 10 appearances in the Scottish Premiership this season, scoring the winning goal against Aberdeen that put Celtic top of the table last weekend.
Van Dijk's form at Parkhead has reportedly attracted interest from England, with Manchester United and Arsenal both linked with moves for the defender.
However, De Boer, who played one season for Rangers during his playing career, has advised his fellow Dutchman to remain with Celtic.
"When Virgil signed for Celtic, I knew he had everything to go on and be a top central defender, both in Scotland and in Europe," the Ajax head coach told the Daily Record.
"I thought he had the attributes to go on and become one of the best players in the SPL, so it is no surprise to me that is exactly what he has done.
"It is also no surprise to me that he is being linked with clubs like Arsenal and Manchester United. They are both in the situation where they could use another top central defender and they are not easy to find.
"I am sure that he could be a success for any club in Europe.
"But Celtic will know exactly what they have and no coach will ever want to sell in January.
"It is such a difficult window to sign players, that you don't want to lose your best one during it.
"It would be good for him to win trophies in the SPL first, before he thinks about anything else, it will all be a part of his education."
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