The 22-year-old Dutchman has been a huge success since joining from NAC Breda for £2.6 million last June and has been linked with a summer move to the Barclays Premier League, where clubs such as Manchester United and Manchester City are thought to be interested.
Lawwell, however, has informed the player's agent, Henk-Maarten Chin, that Van Djik would be best advised to follow the example of Victor Wanyama, who excelled in his second term at Parkhead and was rewarded with a £12.5m move to Southampton.
"My view is that one year is far too early for him," said Lawwell, who also expects interest in keeper Fraser Forster to intensify following the World Cup. "He needs another year in the Champions League. He has to develop here. We have a manager here [Ronny Deila] who will make him better.
"We don't want to sell him. You can take a player and say he isn't going and then someone comes in the back door and he's offered four and five times his money. That turns players' heads. But if I was his advisor I'd be saying, 'forget this year, let's stay and develop'. Then bigger and better things should happen the following year."
Meanwhile, Celtic could delay the unfurling of the Premiership flag for at least a week as Parkhead's post-Commonwealth Games transformation may not be complete in time. This year's campaign is scheduled to commence on August 9, but Celtic are in discussions with the SPFL about staging their celebrations seven days later. "If we think the pitch isn't going to be ready we'd try to play somewhere else on the ninth," Lawwell said.
Also on the cards is a Murrayfield friendly to adjust to the pitch ahead of the Champions League qualifiers. "If we get the right date then it makes a lot of sense to play there before we go competitive," Lawwell said.