The Bayern Munich keeper has been struggling with a shoulder injury in recent weeks but Kopke has allayed any fears that he might miss their Group G fixture on Monday.
"Manuel's going to train fully today so that he can get a feel for his shoulder," he told the press on Wednesday.
"Things are going in the right direction for him. Manuel is experienced enough and we're constantly discussing how his shoulder feels.
"It's not the case that he doesn't have faith in it. Manuel is fully fit."
Neuer's understudy, Roman Weidenfeller, played in Germany's last two warm-up games - a 2-2 draw with Cameron and a 6-1 thrashing of Armenia - and Kopke insists that there is no problem between the two keepers as they battle it out for the No.1 jersey.
"You've got to have a great team spirit," he continued. "Roman has said himself that there is no point in arguing about who should be No.1.
"He would be ready to play at any time but he knows the overall situation. The players are pushing each other to greater things with their performances."