Gareth Barry has already sealed a permanent transfer to Everton following his successful loan move from Manchester City last season.
Ferencvaros midfielder Muhamed Besic is expected to complete his move to Goodison in the next week after linking up with the squad for pre-season training on Thursday.
Osman is aware of transfer rumours involving the Premier League club and the 33-year-old is confident manager Roberto Martinez will draft a few more players.
"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,” Osman 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."
Another player linked with a permanent move to Everton is Romelu Lukaku, who enjoyed a successful loan spell from Chelsea last season, netting 16 goals.
Osman added: "It would be good to have Romelu back. We know the quality he's got.
"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."