Mostly no, in part because I don’t like some of the hype around the PL and the (perceived by me) as disrespect towards other leagues although that is probably more a social media/broadcaster thing than matchgoing fans in fairness.
As well as that not really liking the sides outside of my own (Chelsea) that often make the Champions League.
I’d probably have to actively have a soft spot for the English side or really dislike the non-Prem side to be cheering on the English team outside of Chelsea.
Sky get most of the first picks I think and Man Utd are a huge club globally, Liverpool probably 2nd biggest in the PL. Would be interesting seeing the stats on how often Man Utd are playing on Sunday at 4.30pm over past seasons when Liverpool play Saturday lunchtime. Man Utd playing 4.30 Sunday this weeeknd, and for Merseyside derby Man Utd were on Saturday night but if not mistaken that was moved from Sunday(?) There was only a 2pm kickoff on that Sunday.
Man Utd were not televised in UK when Liverpool played Wolves in Saturday lunchtime slot