If Manchester City wins the championship and wins the trophy, the pointer for Liverpool will only turn to the UCL final. If they lose to Real Madrid in the UCL final, this will be a season that Liverpool will remember for many years. But if they beat Real Madrid and win the UCL cup then they will make up for the Premier league second place.
Of course every history of the Club will always be remembered by the fans. Statistics will always be recorded and will be history that will not be forgotten. So far I think Liverpool have a chance to win the UCL as long as the game is not over. Although actually I support Madrid more to win the UCL title this season. There were still seven days left, now was their last week of competing in the Domestic League.
I can't say who is really favorite to win. The bookmakers indicate that Liverpool has a slight advantage, but Real Madrid has made much more impression in the tournament. Liverpool have had a very favorable draw and haven't actually beaten any level opponent yet. They were even 2-0 behind at half time against Villareal. So I would say Real Madrid is actually the favorite here. Also in a much better flow at the moment.