Mancini, who led Italy to their last success by winning EURO 2020, had signed a contract with the Qatari side until 2027 after an unsuccessful spell with the Saudi national team.
Italian media report that Mancini is the favourite to coach Italy, with the four-time world champions seeking to regain momentum after failing to qualify for a third successive World Cup.
In April, Gennaro Gattuso left the job of Italy coach after a World Cup qualifying defeat to Bosnia & Herzegovina and the team have since been led by Silvio Baldini, who stepped up from under-21 manager to fill the gap.
Despite winning the QSL, Al-Sadd failed to reach the final four of the AFC Champions League Elite and lost in the Qatar Cup final.