Corriere dello Sport says Moratti is determined to test the water with Cesc's representatives about a summer move to Italy.
Moratti was encouraged last week, when Cesc refused to commit himself beyond the end of this season to Barca following their Champions League humiliation at the hands of Bayern Munich.
A return to Arsenal has also been mooted for Cesc, who has been house-hunting in London in recent weeks.
Can Moratti tempt Cesc to Inter? Give us your shout below...