Van Dijk, signed from FC Groningen for £2.6m in the summer, has been commanding at the heart of the Celtic defence since an inauspicious performance in the away leg against Shakhter Karagandy in a Champions League qualifier.
He now faces scrutiny by Ajax attackers and his national manager in a Group H match on Tuesday. The Celtic manager is confident that his defender, who has played at Under-19s and U-21s for his country, can make the step up to full international level.
"I'd like to think Virgil would get a chance with his country," said Lennon. "Holland are a top, top team but for me he's been exceptional this season. He's got everything you want in a modern-day centre half. He just gives us an extra dimension. His physical presence is great and unlike a lot of Dutch defenders he actually likes heading the ball.
"He's got a great spring and timing and he's been pretty dominant for us. He just needs to keep going and keep catching the eye. Certainly his performances in the Champions League will do that."
Of the presence of Van Gaal at Parkhead, Lennon said: "I don't want to put any extra pressure on to Virgil, but I think it is inevitable if he keeps going and progressing the way that he is just now that he will become a Dutch international. He is a natural, a quality player."
Lennon was immediately impressed by his signing on their pre-season tour.
"You could see it from his first day in training, or in the first game against Cluj in Germany. He makes it look easy. People seem to think he has a laid-back attitude, but his work ethic is very high and he's a kid who wants to get better. We've been delighted with him."
With the unplanned departure of Kelvin Wilson to Nottingham Forest and the long-term injury to Steven Mouyokolo, the young Dutchman has forged a good partnership with Nigerian Efe Ambrose in central defence. "The two of them have dovetailed very well," said Lennon who is likely to keep the pairing intact against Hibernian this afternoon.