Rooney has been linked with a move to Everton for a considerable amount of time, with his Manchester United future up in the air.
The England captain, who reportedly earns £250.000-a-week at Old Trafford, has struggled to break into United’s first-team this season, with Jose Mourinho favouring other options.
And Osman is hopeful that Rooney will return to Goodison Park in the coming months.
“I’d like to see him in an Everton shirt,” Osman said. “I think he’s got a lot to offer, moving forwards. Everton have a lot more games now, so there is an opportunity for him to play more games.”
Rooney broke through at Everton, before joining United back in 2004.
There are some question marks over where he would now fit in if he was to move to Everton.
But Ronald Koeman’s side do have European football to contend with next season, meaning the demands on their squad will be increased.
Everton are said to have plenty of funds to spend this summer, as they aim to improve the quality of their team.