Luis Enrique announced earlier this month he would leave the La Liga giants at the end of the season, having been in charge since 2014.
His replacement has been speculated frequently since, with Allegri – a two-time Serie A winner at Juve – among those linked.
But Fernandez denied that on Monday, telling Cadena SER: "It is not true that [Allegri] is coming."
However, he was more open regarding other candidates, including Barca assistant Juan Carlos Unzue and Athletic Bilbao coach Ernesto Valverde.
Fernandez hinted that both would be good replacements for Luis Enrique, who has won eight trophies during his time at Barca.
"[Unzue] is someone who knows the club really well, including the system and the players, so he is prepared," he said.
"Valverde has had several good seasons, not just at Athletic Bilbao."