After Unai Emery was removed from his position in the dugout on Friday, Nuno quickly emerged as one of a number of potential successors to the Spaniard.
In his two-and-a-half years at Molineux, Nuno has transformed Wolves from a Championship outfit into a team which have just qualified for the last 32 of the Europa League.
However, according to The Times, the Gunners board have reached the conclusion that the Portuguese is not the right fit for Arsenal's philosophy.
The report adds that the current intention is to provide interim boss Freddie Ljungberg with an extended period with the first-team squad.
Much could depend on how the Swede fares in fixtures against Norwich City, Brighton & Hove Albion and West Ham United, which come before a showdown with Manchester City at the Emirates Stadium.