According to Colombian journalist Pipe Sierra, the Blues are trying to sign Vidal on a cut-price deal as his current deal has run down to the last 18 months.
"The negotiation began with a first offer of €37m [£33m], the Germans want €60m [£53m]."
The Chilean has 120 appearances for Bayern since joining from the Old Lady in 2015.
Bayern have publicly stated their desire to sign the 22-year-old, who is out of contract at the end of the season. Liverpool, Barcelona and Manchester United have also shown an interest in recruiting the Germany international.
When asked about whether he would try to sign Vidal this month, Conte told the press: "I must be honest, it's not right to talk about a player of another team. Especially if you try to link this player with us.
"But Arturo is a fantastic player, I have a great respect for Arturo, and we spent many years in Juventus together.
"If we go to war, I'd always want him with me."