Henry, the club’s all-time leading goalscorer, was offered a variety of options to take up the position – including one day a week – having been working with the youth set-up for four days a week.
However, Wenger was unwilling to allow his fellow-Frenchman to combine the position with his work commitments at Sky and the offer has been rescinded.
Henry, seen by many as a possible successor to Wenger, has a statue outside the Emirates after scoring 228 goals in 376 games over two periods with the club which saw him win two Premier League titles and three FA Cups.
The former Juventus and Barcelona striker, capped 123 times for France, joined Sky early in 2015 and works across a range of football programmes including Super Sunday and Monday Night Football.
He will now continue to offer his opinions and insight, forged from a hugely successful career which ended with a four-year stint at New York Red Bulls, in a line-up of Sky Sports experts which includes Jamie Carragher, Jamie Redknapp and Graeme Souness.