Here is a quickly little drawing on how you could attach the fiber optic strands to the LED's. The fiber optic strands are red, the LED is blue, and the heatshrink is green. You could drill a little hole in the end of the LED just about 1/16" deep (a few mm's), superglue the strands of fiber optic into the hole, then to help secure everything slide a piece of heatshrink over the whole thing and heat it up.

If you are going to try this or inshaala's suggestion, you must put a resistor inline with the power source (battery, power supply, etc) and the LED so the LED doesn't burn out. The value of the resistor will be determined by the voltage of your power source and the current rating of the LED that you have chosen.

Matt