Wright, 52, pleaded not guilty to two charges of accepting a bribe, dated between April and Septemeber 2016.
Two other men, agent Dax Price, 47 and Giuseppe Pagliara, 62 also denied claims.
The allegations have been made after work by undercover reporters at the 'Telegraph' newspaper investigating corruption in the game.
Former Barnsley assistant manager Wright played for Leeds United and Leicester City among others in a long career, he was appointed at the now League One Club in 2015 and was still in his position there when the alleged bribery is said to have taken place.