A move for Alvaro Morata of Real Madrid was also rebuffed and, at present, seems very unlikely to be concluded during this transfer window after the forward started against Chelsea in their friendly clash on Saturday night.
Chelsea played against Real in the International Champions Cup, in Ann Arbor, Michigan, before a crowd of more than 100,000 in a stadium known locally as The Big House.
Conte’s efforts to lure Carlos Tevez back to English football also failed with a pledge from the Argentine to stay at Boca Juniors.
Lukaku is the last of their big targets still alive and although Everton have valued the 23-year-old at £75m Chelsea hope to complete the deal with a package of around £60m.
The Belgian moved to Stamford Bridge from Anderlecht for £18m in the summer of 2011 but started only one Premier League game for the club.
He was loaned out to West Bromwich Albion and Everton before making the move to Goodison Park permanent, two years ago, for £28m.
Last year, in all competitions, he scored 25 goals.
Chelsea have already signed Belgian striker Michy Batshuayi from Marseille and midfielder N’Golo Kante from Leicester City, both for £30m.
Lukaku would take the number of Belgium internationals at Stamford Bridge to four, with Batshuayi, Eden Hazard and Thibaut Courtois already in the squad.
Costa has been keen to re-join his former club Atletico Madrid but Chelsea have insisted he is not for sale.
Atletico completed the signing of French striker Kevin Gameiro from Sevilla for £28m on Saturday, which indicates they may have given up on landing Costa.
Costa has been unable to train properly this week due to back pain and was told by Conte he will not play until he can train fully.