The versatile former Manchester City player made three first-team appearances under Pep Guardiola before moving to Turf Moor last summer. The 20-year-old England youth international has made six appearances since joining Vincent Kompany's side and arrives in Leith days after Ryan Porteous moved to Watford.
Non-league Wrexham are still in the competition and face Sheffield United in a replay following their thrilling 3-3 draw
The former AC Milan and Napoli manager ends his short reign with Valencia languishing in 14th in the table, only one point above the relegation zone. The 45-year-old's final match was a 1-0 away defeat to Real Valladolid on Sunday. Voro takes control of first-team duties, his eighth caretaker spell in charge at Valencia.