Career
Born in Pistoia, Tuscany, Moncini and Niccolò Arcangioli were signed by Piedmontese club Juventus in 2011, initially in temporary deal from Tuscan club Prato. In June 2012 Juventus signed Moncini outright, for €200,000. In August 2013 he was signed by Serie B club Cesena in temporary deal.
He also made his first team debut in Serie B on 8 November 2013.
On 30 January 2014 Cesena signed Moncini in co-ownership deal, with Stefano Pellizzari moved to opposite direction. Both 50% registration rights of the players were valued for €1 million.
On 18 June 2014 Moncini joined Cesena outright for €750,000, as well as Pellizzari to Juventus outright for €750,000.