The Italian giants have already sealed their third successive Serie A title and can extend their winning streak to seven league matches in this weekend's season-ending clash.
Conte has been linked with a host of European clubs during his tenure in Turin and speculation over his future has risen in recent weeks.
Pirlo credits Conte for playing a key role in Juve's recent dominance and wants him to stay at the club as they target European success.
"He has given us so much and I hope that Sunday is not his last game in black and white," Pirlo told Sky Sport 24.
"In three years he has taken us to three league titles, so I hope it is not his last game."
"More or less we have reached an agreement on the contract," he added.
"I hope the announcement is made in the next few days."
The pair have combined for 34 Serie A goals and the Italy playmaker – who is desperate for his side to reach the 100-point mark with a draw or win against Cagliari – has been impressed with their contribution.
"Our strength? In a team that was already united in spirit we have inserted Tevez and Llorente," he continued.
"We have the opportunity to reach 102 points and we will not let it escape us. It's an important milestone."
