Antonio Conte was eager to add Van Dijk and Lukaku to his ranks during his time at Chelsea.
Conte spent two seasons at Stamford Bridge from 2016 to 2018 and won the Premier League and FA Cup.
He was then replaced by Maurizio Sarri after a widely-reported disagreement he had with the club’s hierarchy.
Conte told The Telegraph: “I asked for two players and we were very, very close after we won the league.
“One player was Romelu Lukaku, the second player was Virgil van Dijk, and these two players were very, very close.
“We were in contact every day and I always said that with these two players we would improve my team by 30 per cent.
“I think maybe we lost the momentum to bring Chelsea at the very top and then to stay for many years.
“It was a pity that it didn’t happen and Romelu is showing with Inter that my idea was right and also Van Dijk has shown with Liverpool that my idea was right for the club.”
He added: “For sure, it would have been a different story if I was the coach of Romelu.
“Romelu is an incredible player and he has a lot of space for improvement.
“In one year at Inter, he had a lot of improvement because he wants to learn and I think I am a teacher. But he can continue to improve to become one of the best strikers in the world.”