Italian media has been awash with speculation Inter are trying to tempt back Mourinho, who won the treble with the club in 2010 and is widely expected to leave Real Madrid at the end of the season.
Mourinho is also being linked with another former club in Chelsea and did little to dampen talk this week when he told Britain's Sky TV that the London club and Inter were "in my heart".
"With Mourinho there has only been friendly text messages, but not for a project. A return in the future? Who knows?" Moratti told reporters on Wednesday while discussing 37-year-old rookie Stramaccioni, promoted from the youth team last March.
"I think he will be confirmed for next season. It means that I have faith or I have learnt something."
Stramaccioni has endured an up-and-down year in charge with Inter fifth in Serie A after spells of huge highs and huge lows. They host champions and leaders Juventus on Saturday.
Inter also lost to Tottenham Hotspur in the Europa League last 16 after going down 3-0 away, only to win 4-1 in the second leg.
Moratti also said he had "no regrets" about letting in-form striker Mario Balotelli move to Manchester City in 2010 and then allowing rivals AC Milan to bring him back to Italy in January.
"We knew we wouldn't take him back because of what happened in the past but there is admiration for him and I am happy that he is becoming more professional - that was the only problem he used to have," the club president said.
The 22-year-old netted a screamer in Italy's 2-2 friendly draw with Brazil last Thursday before scoring both goals in a 2-0 World Cup qualifier in Malta on Tuesday.
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