Zaza has scored 13 goals in 33 La Liga games for Valencia this season and his return to form has led to speculation about his future.
The 26-year-old opened the scoring for Valencia as they beat Deportivo La Coruna 2-1 on the final day of the season on Sunday and he subsequently dismissed talk about a move away from the Mestalla.
“I hope it’s not my last game here,” Zaza told BeIn Sports after the match.
"Others talk about my future, I don’t speak, but I'm good here, I get along with everyone and I want to be here, every time I'm happy, but we've won and we've enjoyed it.”
His agent and father Antonio shared a similar sentiment earlier this month amid reports Lazio, in addition to Milan, were showing an interest.
“He is very happy at Valencia and the only certainty is that he has a contract to 2021 and intends to respect it. His season has been positive, he scored 12 goals and gets on well with the fans. Let’s not forget he also really likes the city," he told Calciomercato.com .
“I don’t know (Milan director Massimiliano) Mirabelli, nor can I say he contacted me to talk about Simone. At the moment, he is thinking only about Valencia, but if the club were to say he’s on the market, then that could change.
“For now, there’s nothing concrete. I only read about Milan and Lazio in the papers, but until calls come in, it’s premature to talk about potential options.”
Zaza was called up to the Italy squad by new coach Roberto Mancini on Saturday , having made just one appearance for the Azzurri since his bizarre penalty miss at Euro 2016 against Germany in a quarter-final shoot-out.