But Inter's exit from the Champions League after being held by PSV on match day six has swelled the pressure on Spalletti as Chinese owners Suning Holdings Group aim to return the club to their former glory.
The pressure mounting on Spalletti has come amid Mourinho's departure from Manchester United and a return to the San Siro, where he won two Serie A titles and the Champions League, has been suggested.
Sporting director Piero Ausillo denied having interest in the Portuguese coach earlier this month, and has reiterated that Spalletti still has the club's backing.
"Mourinho? He is not a shadow," Ausillo told Sky Sport Italia. "It does not surprise me that we talk about him in a time when media and everyone need to say something.
"We work in a more rational way. Our project has been ongoing for a year-and-a-half with Spalletti and will go on with him for many years.
Inter's Chinese ownership have made a significant investment to return the club to the Champions League.
Joao Mario, Matias Vecino and Radja Nainggolan are among those to have arrived for big-money fees but the project at Inter is only part of the way through.
"Suning [Holdings Group] is ambitious," added Auslio. "They want an Inter that returns to winning ways, not one that is content to be second, third or fourth.
"What we can say to the fans is that we are working hard to get Inter back to winning ways as soon as possible."