I am a small-business owner. We provide medical insurance to our
employees. The employee contribution to the insurance is deducted on a
pre -tax basis using a section 125 cafeteria plan. One of our
employees does not want to enroll in our medical insurance plan, since
he has an individual plan from a different company. The individual
plan is cheaper than the company plan. The employee wishes to pay his
premiums using pre-tax dollars. Is this possible ?

Simply, NO.  The employee cannot use their own health plan for pretax
purposes.  You have a "master plan" in place.  You might want to
calculate the difference in the premium amount on a montly basis and
calculate how much money in taxes the employee is losing since it
would not be considered a pretax plan.  Just a suggestion.