Moratti was expected to either confirm the 37-year-old in the San Siro hotseat or dismiss him in favour of a new coach - reported to be former Napoli boss Walter Mazzarri - earlier this week.
But the oil tycoon has so far been unable to meet with Stramaccioni, who has missed several training sessions due to a bout of flu.
Moratti told inter.it: "There is no meeting arranged with Stramaccioni, he's not around and he's not very well.
"Have I already made a choice? Listen, I know this is football but it feels like you're asking me that question every 10 minutes. I will be the one to tell you when it's the right time."
When he recovers, Stramaccioni will have a lot of explaining to do at Inter's headquarters in central Milan.
The Roman coach oversaw eight defeats from 11 - and a total of 16 in a dismal campaign - to leave Inter in ninth place and without any possibility of European football at San Siro for the first time since the 2000-01 season.
And the sudden availability of Mazzarri, who decided to leave Napoli after securing the runners-up spot on Sunday, could prompt Moratti to call time on Stramaccioni's 14-month tenure.