Should I message a manager of another department while in the middle of internship interviews?

I am a current college student applying for summer internships, and I just had an interview at a pretty prestigious company that would be my top pick for an internship. However, the initial phone interview was with an actual manager and not HR and while the team sounds interesting, it wouldn’t be my first pick of what I’d like to work on there.

I saw a manager for a different department viewed my Linkedin profile a few days ago, and based on their profile, their team is directly related to my interests and prior experience and I would really like to do what they do. Is it okay to send this person a LinkedIn message saying I saw they viewed my profile and that I’m interested in their department if they’re hiring interns? Or should I not because of the interview I already had?

During the interview I already had, I asked the interviewer what the next steps would be, and they said that there are typically multiple phone interviews for internships. I’m not sure if this means another interview with the same manager, or if multiple managers may interview me anyways. I didn’t have time to ask more questions, but I did get the interviewer’s email and could ask if needed.

The bottom line is that this is my top company and I would be excited to receive any offer. Still, I would really like to try and speak with this other person, but I don’t know if it’s rude to do so.

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