A deal with the midfielder's club Ferencvaros has yet to be formally announced but the 21-year-old has travelled to Thailand with Roberto Martinez's side
The 21-year-old, who featured for Bosnia-Herzegovina at the World Cup this summer, has not yet been officially unveiled as an Everton player, with a €5 million transfer from Ferencvaros still to be announced.
Roberto Martinez's side face Leicester City in Bangkok on Sunday and while Besic will not take part in the match, the midfielder will be with his new team-mates in order to work on his fitness.
"The next few days will allow Mo to meet the players, but more importantly it is an opportunity for him to get into optimum condition ahead of the new season," Martinez told the club's official website.
"I am looking forward to introducing him to the Everton fans when we come back but first I would like to thank Ferencvaros for the way in which they have approached the negotiations.
"They have been very understanding at this point and we have enjoyed a good working relationship."
Ross Barkley is also part of Everton's pre-season squad after returning from holiday following his World Cup campaign with England.