Juve had already secured the championship thanks to Roma's spectacular 4-1 collapse at Catania on Sunday but, as his players celebrated on the pitch in front of the fans, Conte remained cagey about what next season holds.
"It's been an extremely tiring season. I doubt Juventus could've done any more than this over the past three years," Conte told Sky Italia.
"We need to sit down and talk about it in a calm manner. What I want to say I'll say to the president and directors."
There has been intense speculation about Conte's future in Italian media for weeks, with Conte himself refusing to give a firm answer when pressed.
Juve fans chanted "Conte, stay with us!" during Monday night's stroll, which was decided by a 72nd minute Simone Padoin strike, but there now appears to be serious doubt that he will.
"I have a great relationship with the board," he said. "So we'll assess what needs to be done for the good of Juve, which is what I want, and if I have the strength to carry on."
This was not what supporters wanted to hear on a night they were celebrating what they claim is their 32nd championship, the 2005 and 2006 titles stripped from the club after the calciopoli matchfixing scandal not forgotten.
Juventus have been reborn under the 44-year-old, who won four league titles and a Champions League in 13 years as a Juve player.
They finished seventh in the two years before he arrived as the aftershocks of calciopoli were still being felt at the club. Now they are Italy's dominant force again after three exceptional seasons.
The natural next step would be to restore the club as a European force and supporters would have been hoping to do it with Conte at the helm.
"This is only the second year that we're taking part in Europe and I think we've grown a lot, we got into the semi finals of the Europa league and I think deserved to go to the final," said Conte.
"But we need to be patient. The fans see us winning in Italy and want to return to being a big player in Europe, but it's not going to be easy.
"I am a Juventus fan, I was even when I was going around the country to work as a coach and learn. I am now that I am the Juventus coach and will be in future. Juventus is my family."
- Sports & Recreation