De Costa joined United just before the transfer deadline closed, but a dispute with Greek club Ionikos means FIFA have been called in to arbitrate.
Leeds are adamant they have signed the player on a free transfer, but Ionikos insist the 23-year-old's contract runs until 2011 and are demanding a transfer fee.
Da Costa has agreed an initial one-year deal with Leeds, but cannot feature in any competitive games until FIFA have granted his international clearance.
The winger is allowed to play in behind-closed-door games, however, and that is why he was able to open the scoring yesterday against Chesterfield at Thorp Arch.
The Spireites equalised, but United claimed the win thanks to a strike by Robert Bayly three minutes from time.
The game also saw former Sheffield Wednesday goalkeeper Lucas start for Leeds after signing a short-term deal.
Lucas, who was released by Barnsley at the end of last season, will provide cover for Casper Ankergren.