The Old Lady had gone into the current league campaign on the back of successive seventh-placed finishes but they are now just seven games away from glory
The Turin-based side have yet to lose in the league this term and are currently one point clear of the Rossoneri at the summit of the standings with seven rounds remaining.
Conte is hopeful that Juve will go on to win the title but he confessed that he is just proud that his players are in this position after the club had gone into the current campaign on the back of successive seven-placed finishes in Serie A.
“We're proud to be Milan's rivals, considering where we started from,” the former Italy international told reporters on Tuesday.
“This extraordinary year has come about through the great work of my players from the start of the season.
“We must give it our all right until the end with no regrets. We need to remain proud of what we've done.
"We never spoke of the Scudetto because that would have been crazy. We just set out to play to our best and then see.
"But now we must play to win, regardless of Milan's results. We want to think big and go for the maximum objective, but the most important thing is to continue giving our all.
“The team has enthusiasm and awareness of its own ability but the best thing has been seeing the joy and pride expressed by our supporters.”
Conte is hoping to treat the Bianconeri faithful to another victory on home soil against Lazio on Wednesday.
“Tomorrow we'll face the team in third place,” he mused. “It will be a tough game and we'll need to be at our best to take all three points.
“Beating them would guarantee our spot for direct Champions League qualification.”
Juve's pivotal meeting with the Biancocelesti in Turin kicks off at 20.45CET.