The Blues are destined for a tough draw in the first knock-out round after missing out on top spot in Group C thanks to a 1-1 draw with Atletico Madrid.
Eden Hazard cancelled out Saul Niguez's header as Chelsea sent Diego Simeone's 2014 and 2016 runners-up out of the competition and into the Europa League.
But despite creating a succession of late chances Chelsea were leapfrogged by Roma on matchday six, after the Serie A side beat Qarabag.
Should Liverpool beat Spartak Moscow on Wednesday [6 December top Group E then Chelsea will face either four-time winners Barcelona, their conquerers from last season Paris Saint-Germain or Turkish giants Besiktas in the second round. The draw for the last 16 is made in Nyon on 11 December at 11am GMT.
Conte, the former Italy boss told reporters: "When you play these competitions and go through to the next round you must be ready to face the best teams. In this case we could play against Barcelona, Paris Saint-Germain or Besiktas.
"But I think we must be ready. This is a fantastic competition, the best tournament and for this reason if you want to go through, if you want to be the main protagonist in this tournament then you must be ready to face every team.
"Our opponent won't be happy to play against us. We'll see what happens.
"I remember during the European Championships  with the national team [Italy] we finished first in our group. We played Spain, then against Germany, an if tee beat them we play against France. Sometimes it is not important.We reach the next round and we must be happy for this."
Mourinho's United topped Group A after coming from behind to beat CSKA Moscow, but the 20-time English champions could face the likes of Juventus, Bayern Munich or Real Madrid when the competition resumes in February 2018.
But the Portuguese coach responded similarly when asked about the prospect of facing the trio. "I don't think the team we draw [in the knockout stages] will be jumping for joy when they see our name," the two-time winner stated.
Chelsea have previous against all three of their prospective opponents in the last 16. The west Londoners have faced Barcelona 15 times in major European competition, knocking them out in their last meeting on the way to clinching their maiden European Cup in 2012.
The Premier League champions have met PSG in each of the last three seasons and while they prevailed in 2014 and 2015, defeats in both home and away legs saw the side from the French capital go through last term.
Meanwhile, Chelsea have Besiktas - the winners of Group G - just twice in their history with both games coming in the group stage in 2003. The Turkish outfit won 2-0 at Stamford Bridge before goals from Jimmy Floyd Hasselbaink and Wayne Bridge ensured the side managed by Claudio Ranieri won the away tie.