According to Rob Draper and Joe Bernstein of MailOnline, Lukaku is likely to cost double the £28 million Everton paid Chelsea to sign him in 2014, so any successful move for the Belgian striker will see the Blues' record £50 million fee paid for Fernando Torres eclipsed.
However, Conte "has made it clear Lukaku is vital to his future plans," especially with Diego Costa's future remaining uncertain given continued links to China, per Draper and Bernstein.
Lukaku, 23, has a remarkable goalscoring record in the Premier League, especially for a player still so young.
In 2016-17, he has returned 24 goals, more than any other forward in the division, to take his career tally to 86, per Squawka:
Despite his knack for finding the back of the net, though, he can drift out of games, as he has been doing recently for Everton, per Bleacher Report's Sam Tighe:
Some may question then whether he is worth Chelsea shelling out more than £50 million to sign, but it seems Conte is intent on snapping him up.
Meanwhile, Chelsea are also reportedly preparing to make a £20 million bid for Sassuolo attacker Domenico Berardi.
Per Steve Stammers in the Mirror, Conte believes the 22-year-old could be a fine addition to his squad for next season, especially with Chelsea returning to UEFA Champions League action. He is prepared to better any offer Juventus might make—the Old Lady have a £15 million buy-back clause on the Italian after selling him to Sassuolo for £8 million.
An under-21 Italy international, Berardi already has a wealth of Serie A experience having been a key part of Sassuolo's first team for the past four seasons.
In 2016-17, he has netted four goals and provided six assists in 17 league appearances, per WhoScored.com.
Berardi would be a fine buy for Conte to bolster his attack as he can play on either flank, though he prefers the right, and boasts the intelligence and flair to become a genuinely top player, especially under the tutelage of the former Juve manager.