Gasperini, 58, is in his second spell in charge at the Stadio Luigi Ferraris having returned in 2013. Ventura on the other hand has been making massive strides with Torino since his appointment in 2011.
Conte to step down after Euro 2016
Antonio Conte last week confirmed that after the conclusion of Italy's tournament he will step down citing wishing to "have the opportunity of coaching everyday" as one of his reasons.
The former Juventus trainer took charge of Gli Azzurri after Cesare Prandelli was given his marching orders following Italy's failure in the 2014 World Cup.
Conte lead Italy successfully through an undefeated qualification campaign finishing at the peak of group H which contained the likes of Norway, Croatia and neighbouring Malta.
He has been heavily linked with the Chelsea job which will become vacant in the summer when Guus Hiddink's short term deal comes to and end but he has been coy on the subject and given away nothing regarding his future other than Chelsea not being the only option.
Mancini ruled himself out of the running admitting "at this time it's impossible" for him to take charge but did say that "maybe in the future" as it is a "good option."
The chances of Claudio Ranieri departing Leicester off the back of the season they've had is also highly unlikely categorically ruling him out also.
Fabio Cannavaro, who captained Italy in their 2006 World Cup triumph, is an outsider for the position as is Italy U-21 manager Luigi Di Biagio.