Belgium striker Lukaku, 21, netted 15 goals for the Merseysiders during the 2013/2014 campaign before returning to parent club Chelsea, who are rumoured to be asking for £30million to let him leave Stamford Bridge for good.
"He's a quality player," said Osman. "He showed that when he came last year and scored a number of goals. We could really do with him back and we hope he's coming back.
"The manager sees that he needs to strengthen and we welcome new players coming in because it adds competition. I'm sure the manager's going to bring more in. As to what positions he chooses to bring them in, that's up to him.
"It's great that the manager is bringing in players and he's bringing in quality players. We've all seen what Gareth Barry can do and we're pleased he's staying."
One man potentially challenging Barry for a midfield role is new recruit Muhamed Besic, a Bosnia and Herzegovina international who arrived from Ferencvaros in a £4.8m deal earlier this week.
Osman said of the 21-year-old new boy: "'Momo', as we call him, is settling in really well. He seems a really good player. I'm sure the Evertonians will be really impressed with him when they see him on the pitch."
This is a complete non-story. You could have published this article at the end of last Season and it would be no more informative. I'm hopeful that Liverpool are relegated this season. So what !- birdman