Vidal arrived from Barcelona ahead of the 2020-21 season as Inter aimed to build on a promising first year under Conte, having finished second to Juventus in the league and lost in the Europa League final.
However, the new campaign has not started smoothly for the Nerazzurri.
They have won just three of their opening six Serie A fixtures to quickly slip off the pace and are yet to register a victory in the Champions League, leaving them bottom of Group B at the halfway stage.
Vidal, though, remains confident silverware is a realistic aim with Conte, having enjoyed success while working with the Italian coach during their time together at Juve.
"I'm not afraid to say the word 'Scudetto' because I have won a lot in my career and I came to Inter to continue doing it," Vidal told Corriere dello Sport.
"I am convinced that we will be able to raise an important trophy. Juventus remains the number one favorite [for the title].
"For the Champions League, we have a lot of confidence and I am convinced that we will go on. So far, we have left two-three points on the road. We have to get them back."
Vidal also revealed how much Conte, who led Juventus to the title in each of his three seasons in charge at the club, was key to him choosing to move to San Siro.
"I am here especially for him," the Chile international said of the Inter boss. "We spent three years with Juventus, we won and that was an unforgettable experience.
"He wanted me; we talked a lot last summer and both he and the club did their best to get me to join Inter.
"I found the same Conte of Juve. He loves football, he makes you feel it and he transmits his passion and his desire to win, with him I am wonderful."
Vidal went on to win league titles in Germany and Spain after leaving Juve, with his two-year stint at Barca seeing him play alongside Lionel Messi.
The midfielder may have now left Camp Nou but revealed he will always have a "beautiful" friendship with Messi, a player he places above long-time rival Cristiano Ronaldo in the debate over who is better.
"There is no comparison. Messi is from another planet," he said of the Barca superstar.
"Of the two years I spent with him in Barcelona, many things remained in my heart. A beautiful friendship was born between us, a relationship that will remain forever. United for life.
"I don't know if Messi will leave Barcelona, but I hope he is happy and makes a decision with his heart."