Canover Watson, who sits on FIFA's eight-member audit and compliance committee, said in a statement quoted by the Cayman Compass newspaper he was confident he would be cleared.
The 43-year-old businessman was arrested by the Royal Cayman Islands Police Anti-Corruption Unit on August 28 following a probe into a hospital contract for swipe card billing technology.
In a statement quoted by the Compass, Watson said: "The allegations are denied. In due course, at the proper time and in the appropriate forum, I look forward to setting out my position in greater detail.
Watson is reportedly a close friend of FIFA vice-president Jeffrey Webb, the president of the CONCACAF grouping of countries from central and North American and the Caribbean.
No formal charges have been filed against Watson who has been released on bail and is due to report back to police on September 29.
FIFA's audit committee is responsible for ensuring the "completeness and reliability" of the global football body's financial accounting.