You have to be careful. You really have to discuss with an outside manager first, regardless of what you are told about any formal rules.
When you move, the new manager will be happy, but the old manager will be pissed, unless he was looking to get rid of you or lay you off, which is always possible.
When you move you should try to move to an area completely outside of the one you are in, because if the two managers have to work together afterwards there will be trouble.
I was at a different company and was recruited by a manager in another group. He was literally waiting outside a meeting room for me to ask me if I would be interested in moving into his group. I did. I didn't really think about it before I did it, it just seemed like a good option for me. But afterwards my old manager had it in for me and I had to finish a project that I was working on for him, so he made things difficult.
The old manager ended up inviting me to his office for a "talk". He invited an HR person to watch as he screamed at me for an hour about nothing. I went into the CFO's office (I was in IT) to complain about the harassment, the HR person actually backed ME up. The old manager left the company the day after I complained.
I can't be sure I was the cause of that, but it could be I was the last straw for that manager and the CFO had already had enough of him. HR does work at other companies.
I have not had any backup from HR at Oracle, but there are other companies where HR actually does something for the employees. Yet another good reason to leave Oracle.