The 20-year-old former Bangor captain has signed a one-year deal with the Swans, but the League One side claim that they don't have to pay a transfer fee.
But Bangor insist they are entitled to a fee under UEFA rules, which state that clubs are entitled to a transfer fee - set by a tribunal if neccesary - for young players who move out of contract.
Tudur-Jones, who made his Bangor debut at 16, made his Swansea debut in last month's friendly draw with Fulham.