Burgui will be spending another season away from the Santiago Bernabeu.
On Wednesday, Burgui joined Sporting Gijon on a season-long loan from Real Madrid, signing with the Asturian club after he spent the last campaign on loan at Espanyol.
Burgui, 22, tallied one goal and three assists through 26 appearances in La Liga last season, 18 of which were as a substitute. Upon joining Sporting, he took to Twitter and expressed his happiness at joining the club, writing: "Very happy and eager to be able to wear Sporting's shirt this season! I'm excited to get started and give everything for the club!"