With just a year left on his contract at the end of the season and interest from Paris Saint-Germain - as well as Conte's well-documented desire to return to Italy - the hourglass appears to be running out on his time in London.
Tottenham have been handed a tough tie against last season's beaten finalists Juventus after topping a challenging group that included reigning champions Real Madrid.
Bayern MUnich will play Beşiktaş of Turkey.
The Spanish champions' director of institutional relations, Emilio Butragueno, told beIN Sports: "It could have been the final, for the power of the two clubs, but that happens in a draw - luck plays a role".
"Then when it will be the moment to play against Barcelona we will start to think of the game against Barcelona". We will see how we arrive at the games.
"I think this type of game is a good chance for every player to show the right value". "Our fans will like it after we were knocked out by Barcelona last season".
Paris Saint-Germain chairman Nasser Al-Khelaifi says that his club will relish the task of taking on Real Madrid in the last-16 stage of the Champions League. It's a handsome challenge for the club.
Who are you backing in this tie? They're a strong team. I like to win and when we lose, I'm not happy.
The Italian side will approach the tie with trepidation, having been eliminated in each of their past five European knockout ties with English teams. "We'll go into it with optimism, confidence and a huge desire to get through".