Fowler has spent most of this season injured after undergoing a hip operation in the summer - he returned to action in December, but has started just two games since then.
The England international appeared as a second-half substitute for United during Saturday's 2-1 defeat at Maine Road and got a great reception from the City fans when he was introduced.
If the Fowler deal goes through, it will be the fifth major departure from Elland Road since Venables replaced David O'Leary as manager.