Drain pineapple, reserving juice; set aside.
Combine 2 teaspoons reserved pineapple juice, mayonnaise, and ginger; stir well.
Cover and chill.
Combine remaining pineapple juice and teriyaki sauce in a shallow dish; set aside.
Place each chicken breast between 2 sheets of wax paper, and flatten to 1/4 inch thickness using a meat mallet or rolling pin.
Cut each breast in half; add to teriyaki sauce mixture, turning once to coat.
Cover and marinate 2 to 4 hours in the refrigerator.
Remove chicken; reserve marinade.
Broil chicken 5 inches from heat, 2 minutes on each side, basting once with reserved marinade.
Top each chicken piece with a slice of cheese and pineapple; broil until cheese melts.
Place chicken on bread; spread each open faced sandwich with seasoned mayonnaise mixture, and top each with 1/4 cup sprouts.