Smith, together with Derby's chief executive Keith Loring and secretary Keith Pearson, will meet the Department for Education and Employment's (DoEE) independent three-man Football Appeals Review Panel in Sheffield.
Kinkladze, the Georgian midfielder who was outstanding for three years for Manchester City, does not meet the necessary requirements because of a lack of international appearances, so the club have gone straight to the appeals committee.
Derby are hoping to persuade the DoEE to give special dispensation to the 26-year-old, who is on loan from the Dutch club Ajax until the end of the season.
The Rams are hopeful of gaining a permit for Kinkladze, who has returned to his native country until the hearing is over, and a decision is expected tomorrow or Thursday.
The case has similarities to that of Juninho's earlier this season, when Middlesbrough were given permission to sign the Brazilian despite the fact that he had not played in enough international games.
The arrival of Kinkladze would be a welcome boost for Derby ahead of Sunday's tricky Premiership match at Arsenal. The Rams have Deon Burton, Steve Elliott and Kevin Harper back from suspension for the game, though they will definitely be without the services of the injured Stefano Eranio and Lee Morris. Mikkel Beck is still on loan to Nottingham Forest and Esteban Fuertes has been deported because of a passport discrepancy.
Meanwhile, Smith faces a wait to see if he will be hauled before the Football Association for comments attributed to him following his side's 2-1 loss to Manchester United on Saturday. Mike Reed sent off Stefan Schnoor and booked four other Derby players, and the Rams manager said: "The referee's performance was biased." Steve Double, an FA spokesman, said: "We're waiting for the reports from the relevant people."Reuse content