Liverpool reached the final of the Champions League last season before losing 3-1 to Real Madrid in Kiev. Liverpool claimed one of their most impressive ever European Cup away wins with a 3-1 victory against Bayern Munich in Germany, and Spurs cruised past Borussia Dortmund with a 4-0 aggregate win against Lucien Favre's team.
"I would avoid City", the former Red said on Italian broadcaster Rai Sport when asked which teams Juventus would not like to face in the quarter-finals.
Liverpool have previously taken part in six quarter-finals in the Champions League era, all of which have been post-2000.
And fans of any English club will be left disappointed with Liverpool - should they make it through - Manchester City, United and Tottenham all having over 25,000 season-ticket holders.
"If the draw gives something like Manchester City against Manchester United, or Tottenham against Liverpool, for example, it would be fantastic matches".
"My second choice would be what I think would be fantastic extra motivation, something thy would deserve, I'd do Ajax against Porto", he said.
Juventus' courageous turnaround to send Atlético de Madrid crashing out of the competition impressed the blaugranas, which is why they would prefer not to meet them - at least at this stage.
Ward-Prowse has one senior cap to his name after featuring regularly for the under-21s Credit PA
"I wouldn't like Juventus against Barcelona because I think it would be something really special".
Pep Guardiola's side are widely considered one of the favourites to win the Champions League, despite the presence of teams such as Juventus and Barcelona in the competition.
When asked to pick his outright victor, Mourinho said: "I always say, when you get to the quarterfinal, everyone has the feeling, 'I have 12.5 percent chance of winning'".
"And with the emotion of that game, the Champions League final, can those players even realistically play on the Thursday night for us?"
The draw takes place at UEFA headquarters in Nyon, Switzerland, at 11:00 GMT on Friday, March 15.
A nice spread of interest in the other four teams there, in fairness.