Former Manchester City boss Stuart Pearce added: "I think Liverpool have gone as favourites now for the competition, being that side of the draw".
In an article titled "Barcelona tie is what the Champions is all about", they talk about the "bad luck" which United have faced so far in the draws.
This year is the 20th anniversary of United's treble-winning season, when they won the Premier League and FA Cup as well as the Champions League, with hard moments on the way to all three trophies. Juve will be at home in the second leg.
While Mohamed Salah, Sadio Mane and Roberto Firmino boast a total of 44 league goals between them this campaign, compared to Fulham's team total of just 28, Parker wants his team to be the aggressors on Sunday.
Despite just a single point gap at the top of the standings, Manchester City remain -275 favorites to win the league while Liverpool are +225.
Man United face Barcelona in UCL as Liverpool draw FC Porto
The last five Champions League games we lost is because we didn't defend like we wanted to, but we learn from that. You can watch all the Champions League action exclusively live on BT Sport and across our digital platforms.
Expectations are high that Guardiola, who twice guided Barcelona to Europe's top prize, will lead the Premier League champions into the final four for the first time since taking charge in 2016.
"They came back against Paris Saint-Germain". As the match entered stoppage time, and with Liverpool set to drop two valuable points, they won a penalty which Steven Gerrard coolly converted to send the travelling Kopites home in delight.
Jurgen Klopp will not look to tinker too much with his lineup when Liverpool face Fulham, although he could make minor changes to his midfield. This was against West Ham, for whom Michail Antonio equalised on a night when Liverpool frustrated their travelling supporters at London Stadium.
Leicester City regained their winning ways against lowly Fulham to keep the top spot in moneyline profitability (+12.52 units).
Twelve months ago, City were blown away by Liverpool in a 3-0 first-leg defeat at Anfield before losing 2-1 in the return game at the Etihad.
Mohamed Salah is one goal away from scoring 50 in the Premier League in fewer games than any other player in Liverpool history. At least one of those records will tumble by 4:15 on Sunday afternoon.