To take a shine to someone

to have or develop a fondness or attraction to someone (often on first meeting)

My best friend and I bumped into my cousin in a restaurant and he asked me if I could arrange for him to go on a date with her; he has taken a shine to her.

The idiom is considered to be an American idiom that emerged in 1880s from the phrase “to shine up to someone”. This phrase meant that your nice behaviour really attracted someone so that they might have become fond of you.