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The 28-year-old midfielder could be a Leeds player by the end of the week, he will travel to Yorkshire on Tuesday evening to discuss personal terms and then undergo a medical.
Chairman Peter Ridsdale said: "Nicky is a player Terry admires and wants. He has been playing Harry Kewell in a different position and that has created an imbalance - hopefully Nick will help redress that."
Barmby has previously played under Venables for both Tottenham and England.