Former West Brom youngster Elford-Alliyu, 20, impressed during a loan spell at Gigg Lane last season, scoring twice in four starts and nine substitute appearances.
He joined the Shakers on a free transfer in the summer but has not started a game since the League One opener against Brentford and made the last of his four substitute appearances in October's 1-0 home defeat to Swindon.
A brief statement on the Bury website read: "Our thanks and best wishes for the future are extended to Lateef."
- Sports & Recreation
- Gigg Lane