Asking an expert in your field that you have never met to review your manuscript I would like to submit my manuscript to a journal. Before I do, I would like to reach out to a professor at another university to see if he would be willing to review my manuscript since he is an expert in the field. 

Is this appropriate or common practice?
Ask your advisor at your own university, but the answer is 99.9% no. It's your advisor's job to look at your paper before you submit.

In some cases it's appropriate to share with outsiders when they aren't really outsiders but rather collaborators or colleagues known to you or your advisor. In other rare cases you might reach out to someone whose work is very similar or affected by yours, but again, this would be at your advisor's direction.



edits:

OP clarified in a comment that their advisor has reviewed their paper and found it suitable, but the paper is outside the advisor's best expertise. In this context, I do think it is worth getting an outside opinion if the advisor agrees, but I still would not suggest cold-contacting anyone.

Instead, I would recommend asking the advisor if someone in their network might have more expertise in the specific area, even if they aren't the very top person in the field. The point is to get an informed opinion from someone friendly but willing to be honest.

Another option is to do some networking at conferences, etc. In that way, you turn people you've never met into people you've met and it may become more appropriate to ask (and certainly more likely to get a positive response).