The highly-rated youngster remained at the Etihad Stadium as the transfer deadline came and went, but there is still a chance he could be on the move in the coming weeks.
The emergency loan window is due to open for clubs outside of the Premier League, and Manuel Pellegrini is keen for Barker to go and get some regular game time under his belt.
There is no shortage of interest in the talented winger but Leeds boss and former City star Uwe Rosler, will be hoping to use his connections to take him to Elland Road.
Pellegrini will want guarantees over the amount of game time Barker will get, but there is a good chance the youngster will be heading over the M62 to West Yorkshire.