Lukaku scored 16 goals as the Toffees finished fifth to qualify for Europe for the first time in five years.
Osman, 33, is desperate for the Belgium international to be back at Goodison Park in time for his testimonial game against Porto on Sunday, 3 August.
"It would be good to have Romelu back - we know the quality he's got," he said.
"There might be a bit more to do to get him back here but it would be great if he could come back in time to play in the game."
Everton's only signing of the summer is Gareth Barry, who also spent last season on loan with the club, although they are close to completing a deal for Ferencvaros midfielder Muhamed Besic.
Osman hopes manager Roberto Martinez can make further signings.
"We try not to be distracted by speculation, but sometimes you can't help but hear the rumours about who the manager wants to bring in to the club," he said.
"Besic should be completed in the next few days and we're aware of the rumours about a couple more coming in. It would be good if any new arrivals could play in my testimonial."
Everton midfielder Leon Osman hopes striker Romelu Lukaku will return to the club after impressing on a season-long loan from Chelsea.