The 36-year-old played in Italy between 2014 and 2016, after his time in Manchester came to an end, and he has spoken of how shocked he was that Milan are not Inter's biggest rivals in the league.
"I was shocked that Inter-Juventus is a bigger derby than Inter-Milan," he said, as quoted by the Sun.
"They call it the derby of Italy and it’s the biggest rivalry by far. Players go between the two Milan clubs but if you change between Inter and Juventus..."
The former Serbia international has also spoken in defence of Manchester United midfielder Paul Pogba, following the 24-year-old's struggles at Old Trafford.
Vidic played for United from 2006 to 2014 and revealed he believes it is not Pogba's fault he hasn't performed as expected for Jose Mourinho's side.
The Red Devils broke their transfer record to sign the France international, splashing out £89m
in August 2016, and Vidic believes the price tag may have put too much pressure on the former Juventus midfielder.
“It is not the player's fault that a club is paying so much money for him. If someone offers you a big contract, you would not refuse, probably,” the former defender told reporters at St George’s Park, as quoted by Calciomercato.
“I think the environment is important - who is around you, for example - to make you better. For the players of 22 and 23 to get so much money and publicity, he must feel like he is the most powerful person in the world. I was a football player, I felt like that: ‘Wow, I am feeling really good’."
The United legend feels Pogba needs the support of his teammates to keep him grounded and help him rediscover the form that warranted a record breaking transfer fee.
He added: “But I think you need to have someone in the dressing room - some of the players - who can help you come through these difficult situations."