If you wanted to ask X the permission to borrow one euro from Y, you would say:

Est-ce que je peux emprunter un euro à Y?

So theoretically you could say:

Est-ce que je peux emprunter un euro à toi?

But most French people would frown after hearing such a sentence since

Est-ce que je peux t’emprunter un euro?

is much more common and sounds more natural.