The experienced coach was expected to announce a new three-year deal at a news conference on Friday (AEST).
But Spalletti, who saw his side secure UEFA Champions League football with a dramatic last-day win away at 10-man Lazio, instead revealed he is happy with the current situation and is yet to pen an extension.
"I have a contract at Inter and I'm very happy," Spalletti said.
"For me, nothing would have changed had we not made the Champions League.
"When you're here, you realise that you don't just sign to guarantee your salary. There's no rush to sign the contract.
"We want to continue to reduce the gap between ourselves and the sides ahead of us. We've already done a lot in this regard. If you look, the statistics on the team's growth are encouraging.
"The club has already started to move in a good way but we have to respect the financial side. Football has changed. Before the end of the month, we'll have to look at the books and strengthen the club, just like everyone does."
Spalletti also admitted Inter will have to reduce the size of its squad before pursuing permanent deals for loan duo Rafinha and Joao Cancelo.
"At the moment, Inter don't have the chance to pay Valencia and Barcelona to buy Cancelo and Rafinha," the former Roma boss said.
The future of Inter captain Mauro Icardi, meanwhile, remains in doubt as the striker is a reported target for clubs, with both Chelsea and Real Madrid rumoured to be interested.
"It depends what he wants, keeping those who don't want to stay is difficult," Spalletti replied when asked about the talismanic forward.
"That’s not the case with him, but I can't sit here and tell you he won't make a request, it depends what happens in the transfer market.
"A professional can consider a different experience. Clearly, if important players leave it reduces your chances to grow, if other important players don't arrive."