The Italian club have been chasing Lukaku during the transfer window and have reportedly returned with a fresh bid of around £65 million ($79 million) as they try and get the deal over the line.
The Belgium striker has not played a single minute of United’s pre-season campaign and Conte is hopeful he can bring the 26-year-old to the San Siro.
“We continue to work on it in the best possible way,” he said after his side drew 1-1 at Tottenham in a pre-season friendly on Sunday.
“I understand there are some gaps that need to be filled but at the moment I am very hopeful that this will happen.
“At the same time I’m working with a great group of players that gives me lots of satisfaction.”
A complication to Inter’s chase of the former Everton striker is a reported swap deal between United and Juventus that could see Argentina attacker Paulo Dybala move to Old Trafford in exchange for Lukaku.
“Honestly I can’t know, I don’t know,” the former Chelsea boss said. “I’m reading (about) this swap in the papers.
“For sure Lukaku, we are talking about a good player, a striker that in the past I tried to buy when I was Chelsea’s coach.
“We’re talking about two big clubs, Juventus and Inter Milan, but honestly I don’t know. Only my way is to work with this group of players, to try to improve this group and instil the right mentality.”