Antonio Conte is demanding the club go on a spending spree ahead of the new season.
With Chelsea returning to Champions League football and losing long-term members of the squad, a period of transition is underway.
John Obi Mikel, John Terry and Branislav Ivanovic will all have moved on within the space of six months.
And Conte is looking for replacements who can bring years of success to Stamford Bridge.
According to the Mirror, Everton hitman Lukaku and Southampton centre-half Van Dijk are top of his wishlist.
The combined price will prove costly, as it is expected Chelsea must fork out in excess of £120m.
But both have shown their quality in the Premier League and are seen as quality additions to Chelsea’s team.
The Blues are battling Manchester United for their former striker Lukaku, who has decided against renewing his Everton contract.
The 23-year-old is on course to finish as the league’s top scorer this season, and could replace Diego Costa in west London should the Spain international leave.
Meanwhile, Van Dijk has been sidelined for the second half of the campaign with an ankle problem.
However, his form prior to that for Southampton since joining from Celtic has drawn great attention from England’s elite clubs.
On his summer intentions in the transfer market, Conte said: “We have to find the right substitutes for these players (Terry, Mikel and Ivanovic) and then work to put these players at the same level.
“We are building. We are building something important. If we are able to take the right player to improve this squad and to continue to work with these players, we can improve for sure.”
