Lukaku, 24, was Conte's priority transfer target of the summer transfer window, but multiple reports emerged on 6 July suggesting that Manchester United had agreed to a £75m ($97m) fee with Everton for the striker.
Sources close to Everton told the BBC that no agreement had been signed with United, leaving Chelsea officials scrambling to see if there is any way back for them.
Citing sources, the Daily Mirror said Conte was "fuming" at the club's inability to close out the transfer after weeks of speculation linking Lukaku with a move back to Stamford Bridge.
The former Italy boss was reportedly in regular contact with Lukaku and was making tactical plans for next season with the 24-year-old leading the attack.
The report added that Conte could consider his future at Stamford Bridge, with sources saying that the Italian tactician genuinely considered leaving last month amid tension with the club's hierarchy.
The Blues have sold Nathan Ake, Juan Cuadrado, Asmir Begovic, Bertrand Traore and Christian Atsu this summer, while goalkeeper Willy Caballero has been the only arrival as a free transfer from Manchester City.
Diego Costa is also expected to leave the club after Conte informed the forward via text message that he was no longer part of his plans last month.
The former Juventus boss was reprimanded by the Chelsea hierarchy for the move, which they feared had wiped out millions off Costa's market value.
Costa is keen on returning to Atletico Madrid, with the La Liga club preparing a £22m-plus-add-ons offer for the Spain international.
The Blues have offered Conte a new contract worth £9.6m a year, although the Italian is yet to put pen to paper.
Arsenal's Alexis Sanchez, Monaco's Tiemoue Bakayoko and Roma's Antonio Rudiger are among the players Chelsea have been linked this summer.