That is according to Belgian journalist Kristof Terreur, who claims the Chelsea manager remains eager to bring the striker to Stamford Bridge.
But the Premier League champions look set to lose out to Manchester United.
Starsport understand that United have agreed a £75m fee with Everton for Lukaku.
The Belgium international has said yes to a long-term contract at Old Trafford worth £250,000-a-week.
Terreur tweeted: "Antonio Conte has been in regular contact with Lukaku in the last few weeks.
"He wants a deal over the line too.
"Over to [director] Marina [Granovskaia]."
Starsport exclusively revealed in May that United manager Jose Mourinho wanted to land Lukaku.
United executive vice-chairman Ed Woodward promised Mourinho he would do his best to beat Chelsea to Lukaku.
Chelsea face starting the season without a big-name striker, with Diego Costa closing in on a return to Atletico Madrid.
The Blues could now turn to Real Madrid striker Alvaro Morata, who was interesting United until their move for Lukaku.
Meanwhile, Chelsea midfielder Nemanja Matic fears his move to Old Trafford could be off.
Starsport understand that United have agreed a £40m deal with the Premier League champions for Matic but the Lukaku saga has thrown a spanner in the works.
