Nuno, 40, ended his playing career in 2010 and as a coach helped modest Rio Ave reach the finals of the Portuguese Cup and League Cup last season, where they were beaten each time by Benfica.
Argentina-born Pizzi was appointed in December to replace Miroslav Djukic, who was fired after a poor start to their domestic campaign.
They reached the semi-finals of the Europa League, where they lost narrowly to Spanish rivals and eventual winners Sevilla, but finished eighth in La Liga and failed to secure a lucrative spot in Europe again for next term.
Valencia, who have been hampered by financial troubles in recent years, are in the process of being bought by Singapore businessman Peter Lim.
Lim, who has a fortune worth around $2.4 billion according to Forbes magazine and is an avid soccer and sports fan, had pushed for Pizzi's dismissal and Nuno's appointment, local media reported.
(Reporting by Iain Rogers, editing by Stephen Wood)
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