I am a few weeks into a new job. I was hired in one department but have been receiving signals from other manager and my immediate boss that the other manager is under-resourced and needs more help than he (my boss) does. I personally would also agree and I also feel that my background is better suited to work under the other manager. How should I approach this situation? Should I be direct about it?
Double check with your manager. I hate hints, because I almost never get them right - I hate people, in particular managers, who talk in riddles but that's another story for another day. I prefer blunt talk, no noise, no guessing: "I think you have been giving me signals that the other manager needs me more than I do. If that's the case, count me in for going where ever I am most needed and most useful. Thanks"
It depends on the signals. If the signals are not very specific and could have other interpretations (e.g. that your time might be split somehow to assist the other manager, rather than switching completely), it might be best not to bring it up until your manager directly raises the issue with you in the form of a question.
When the business need truly arises, the manager will ask you straight up. If this is just something they are mulling over, they might not be ready to make the switch officially and just seeing how you would react. In which case the best strategy may be to remain neutral, i.e. "Since I am new here and am just getting oriented, I guess I could go either way, that would be fine with me."
You don't want to appear too enthusiastic to switch, since that might send the currently manager a wrong message that you'd rather work for someone else than him/her (awkward if future business need will require you to switch back to current manager). You don't want to appear too unenthusiastic either, in case you will in fact need to switch. Just be ambivalent about it and let the managers make this decision, rather than try to make it for them. Good luck!