To fancy someone of something means to like someone or something; if you say you fancy someone, it means you are attracted to them. In football, we use this phrase to talk about which team we think will win a competition (it isn’t often used to talk about one game). At the beginning of the football season, pundits and fans talk about who they think will win the league, who they fancy to win the league. It can also be used to talk about one-on-one battles: Player A fancies her chances against Player B. This means she thinks she can get past or do better than her opponent.
Example: “That’s the big question and the main reason I don’t fancy them (Liverpool) as an each-way proposition at 12/1.” (Football 365)