After 17 goals on loan at West Brom last term, Belgium striker Lukaku top-scored on Chelsea's tour of Asia with four goals, including a double in the 8-1 defeat of the BNI Indonesia All-Stars.
Cahill said: "He had a great loan spell at West Brom last season, has been flying in training and scored two great goals (in Jakarta).
"I don't see why he shouldn't be a Chelsea player. I play against him in training a lot and he's a handful just with his pace and power.
"His finishing is great too. He's still a young lad, but scored a lot of goals at West Brom last season.
"It's exciting times for him and I'm sure he's looking forward to the season."
Another player who impressed in Asia was 17-year-old Burkina Faso international Bertrand Traore, who, due to regulations, is not yet a Chelsea player.
Traore scored in Malaysia and a spectacular goal in Indonesia also announced his ability, with Chelsea poised to sign him as soon as he reaches his 18th birthday.
"It's too early to say he's ready to do this and that, and we don't want to get carried away, but he's certainly not looked out of place in training alongside some top international players," Cahill said.
"He's slotted in nicely. He's a young lad, but I'm sure he's got a bright future at Chelsea."
Cahill hopes to be a key player next term by forming a defensive partnership with captain John Terry in the forthcoming season.
Cahill's bid for a place in Jose Mourinho's first competitive game of his second spell in charge, against Hull on August 18, will be challenged by David Luiz when the squad reconvenes next week ahead of the four-match trip to the United States.
As Brazil defender Luiz - absent from Asia following the Confederations Cup - demonstrated how crucial he is to Chelsea last term, Terry endured struggles with his fitness and in a congested campaign was not guaranteed a start.
But Mourinho believes the team talisman is fit and flourishing in pre-season.
Cahill said: "Last year he had a couple of niggles and hopefully they're behind him, not just for him but the team.
"It seems like I've only played with him in bits and bobs, with him being in and out, and we've not really had a run of games.
"It would be great if he could stay fit so we can have consistency."
Cahill joined from Bolton in January 2012 and is enjoying life under Mourinho, a man Terry knows well having captained the Blues during the Portuguese's first spell in charge.
"It's been exciting to work for Mourinho and we're slowly getting to know him," Cahill said.
"There's a handful of players who knew what to expect from him, but for players like me it's just exciting.
"He's getting to know the lads and we're getting to know him. From the first game to now we've been getting better.
"The lads spoke very highly of him before, even before he was linked with the job, just with me asking about him.
"Just like the fans are excited, the players are excited as well."