No, that sounds strange to me.
"I would like", together, is a polite way to say "I want".
"I like", of course, has a different meaning.
"I will like" puts "I like" in the future,
but we rarely have an occasion to say we expect to like something tomorrow that we don't like today.
It occurred to me that if people are really saying "I will like to..." then perhaps they're also writing it. And indeed, a search on Google found many thousand examples.
However, among them there were many whose first language wasn't English (especially examples from Africa), and most of the remainder had other grammar faults that lead me to keep to my earlier conclusion (#7).