Spalletti’s side are the only unbeaten team in Serie A this season and sit top of the league a point ahead of Napoli with six-time defending champions Juventus two points behind in third.
Manchester United boss Mourinho led Inter to the treble of Champions League, Serie A and Italian Cup titles in 2010, and also won the league title with the club in 2009.
“You have to stop it. I’ve been here for two days, and he made Inter history,” said Spalletti, speaking ahead of Tuesday’s Italian Cup game against Serie C side Pordenone at the San Siro.
“I can’t come close, so do me a favour: don’t put me close to him. Mourinho knows too that it doesn’t stack up,” added Spalletti.
Spalletti is in his first season at Inter but won the Italian Cup twice with Roma in 2007 and 2008 and two Russian league titles with Zenit St Petersburg.
He said he was expecting a tricky last-16 Cup clash against Pordenone who eliminated Serie A side Cagliari in the last round.
“Pordenone represent a real danger. We saw it in their game against Cagliari and we all know how good a side Cagliari are, how difficult it was for us against them.”
The Italian Cup last 16 matches will be played throughout December and include six top-flight clashes, including Napoli against Udinese and holders Juventus against Genoa.