Advisor wants me to come up with a research project. I came up with a project, but it's not with him I'm in the second half of my PhD, and my advisor wants me to come up with an original research project.  I also have a mentor (who is not a professor at my university) who has also been telling me to come up with an original research project.

I came up with a project, but it was for my mentor, and not my advisor.  I'm not sure if my advisor would want to work on the project with us, and if he did it would be weird because he wouldn't be the supervisor.

What should I do?  I feel like it would be awkward to talk to him about  this.
The best solution would be to meet up with your advisor and discuss regarding this matter.

As your advisor instructed to find a research project, you did. The project is relevant to your mentor but you are unsure whether your advisor would be interested in the project.

This is a legitimate doubt that only your advisor can clarify.