Ferrara, who is the current manager of Italy's Under-21 side, has been offered a two-year contract to guide the Genoa club.
"(Sampdoria president Riccardo) Garrone has contacted me to make a proposal to Ciro Ferrara, something other club executives had failed to do before," Abete said at a press conference.
"I have spoken to Garrone and to Ferrara, who expressed to me his wish to be involved with Sampdoria in the next couple of years and we have given him the okay.
"With (Italy coach Cesare) Prandelli and (FIGC vice-president Demetrio) Albertini we will consider who the new Under-21 coach will be."
The 45-year-old Ferrara will return to guide a club for the first time since managing Juventus in the 2009-10 season.
Ferrara will succeed Giuseppe Iachini, who took over at Samp last November and led the team to promotion to Italy's top flight via the play-offs last month.