The former Juventus and Chelsea manager took over at the San Siro club at the end of May but has struggled to overhaul a bloated squad in preparation for the Champions League campaign and a tilt at the Serie A title.
Belgian striker Lukaku has been strongly linked in the media with a move from Old Trafford to Italy.
But Conte refused to dwell on reports of his frustration at being unable to land the 26-year-old forward due to a disagreement over the transfer fee.
"Lukaku is Manchester United's player. This is the reality. I have always liked this player, even when I was Chelsea coach and I tried to sign him then, but he is not my player as of now," Conte told reporters in Singapore on the eve of a pre-season friendly between the clubs.
"I can't talk about him out of respect for Manchester United. He would be an important player for us and improve the squad, so we have to see what will happen," added the Italian, shortly after United boss Ole Gunnar Solskjaer confirmed Lukaku would miss the match because of injury.
"It's not easy to start the season without strikers but the market remains open and players will have to come in and go out. But the current situation will mean our upcoming matches will be difficult without forwards," Conte said.
Confirming that out-of-favour forward Mauro Icardi and midfielder Radja Nainggolan were both "out of the project", Conte is looking forward to the big challenge ahead of him despite struggling to instigate a fast flow of transfers.
"We are enthusiastic to start this new project but we are a little bit behind in terms of where I would like us to be on this journey down a long road," he said.
"The transfer delays have made life difficult but we have to also sell some players as well as buying them. I have spoken to the owners and they are aware we need to act quickly."