The Sun says the Hammers were speaking with Nuno, Slaven Bilic and Gary O'Neil about succeeding Potter before the former agreed to the job at second attempt.
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West Ham made first contact with Nuno after defeat to Tottenham over a fortnight ago, but he rejected their approach with a dispute over his payoff with Nottingham Forest rumbling on.
The Hammers then spoke with former Wolves manager O'Neil and also Bilic, a former Irons boss, as alternatives.
But Nuno was always their first-choice and once things were settled with Forest, West Ham quickly to reach terms with the Portuguese's camp.