Osman's testimonial sees the Blues entertain Porto at Goodison Park on Sunday, August 3 in the side's only pre-season fixture in their own stadium
The England international has played at Everton for more than 10 years and says he would relish the chance to share a pitch with Besic or any other new arrivals
Osman said: "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
"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."
Besic is on the verge of becoming Roberto Martinez's second summer signing following a permanent deal for Gareth Barry
The 21-year-old played in all three of Bosnia-Herzegovina's matches at the World Cup and is expected to finalise his switch from Ferencvaros next week
Everton also remain keen on 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.
"T here 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."
Source : PA
Source: PA