Calvin Zola and Gary Roberts have not travelled to Bulgaria with their Crewe team-mates for a pre-season tour.
African striker Zola is concerned about the prospect of re-entering Britain after visa problems in 2004 saw him suspended from action while a solution was reached.
Having only recently seen that documentation re-approved, granting him permission to remain in the country, he is reluctant to put himself in a similar position again.
Zola will now undertake an individual training programme back at Alexandra Stadium.
While Zola's omission from the travelling party was his own decision, Roberts' failure to make the squad was down to first-team coach Steve Holland.
The Railwaymen's boss believes that the midfielder is 'not in the right frame of mind' having recently been transfer listed and decided that it was best for the 21-year-old to stay at home and ponder his future.
"People will say I have a problem with Gary, but every time I could I picked him last season," Holland told the club's official website.
"I picked him more than 40 times and I know the level he is capable of reaching, but as we've said before it is up to him.
"He could do really well in his career, or he could fall frustratingly short but only he can make that decision because he certainly has the ability. It is just a question of him applying himself better."