Keeper Handanovic has been linked to a possible move to Barcelona for a fee in the region of 30million euros (£25.5m).
But Moratti wants the keeper to stay with the Serie A side and has denied the rumours.
He told Inter.it: "I think there is nothing. I read it in the paper too, but I read a lot of things that are not true, I can't deny all of them.
"Should Handanovic remain? Yes."
Another player new manager Walter Mazzarri could draw on is Stankovic, who has cooled growing speculation he could be leave the club by mutual consent after appearing in just three games last season.
The 34-year-old wants to see if he fits into Mazzarri's plans before deciding on his future.
"There is absolutely no truth in that (speculation)," he told Sportal. "As things stand I will start the season with Inter and then we'll see what new boss Walter Mazzarri wants to do.
"A move back to Lazio or a transfer to the MLS? There is nothing. If an offer arrives then I'll think about it, if not then I'll stay another year with Inter."
Meanwhile, the club have announced the contract extension of veteran defender Samuel.
The 35-year-old's deal now runs for another season and Samuel wants to play his part in a successful campaign.
"I hope to repay the club and the supporters' faith that once again believed in me," he told the club's official website.