Perisic has been linked with a £48m switch to Manchester United for the majority of the transfer window so far, and Spalletti himself confirmed earlier this week that the club would listen to offers for the winger.
However, both he and Jovetic - who is understood to be wanted by Sevilla - scored in a 2-1 pre-season friendly win over Chelsea on Saturday, and Spalletti insists that both are more than welcome to stay at San Siro if they want.
"We return after good work, where we started to consider the right attitude to have, but of course you need a series of results to consolidate that," Spalletti told reporters.
"I think it helped everyone. They played and behaved as a team, but aside from the victories they also moved the ball at high intensity with quality and beautiful goals, so that boosted everyone's desire to play for Inter.
"As far as I am concerned, everyone can stay, we just have to see what their intentions are, because along with quality we need them to be ready to form part of a team."
Perisic has scored 18 goals in 70 Serie A appearances during his two-year stay at Inter.