Can you say 'wrap into…'?

Question

In dictionaries I only find the phrase to wrap something up, I can't find any phrase that would express what you wrap something up in.

If you want to express in what you wrap something up, can you say wrap something (up) into something?

You could probably say that you wrap something up with something, but could you also say, for example:

I wrapped the present into the wrapping paper?

Answer 1

No, the usual preposition is "in", not "into":

I wrapped up the present in wrapping paper.

You could say "I put the present into the wrapping paper", but that is not what the verb "wrap" requires.