Any major that you like and can do well in, and which you can take the pre-med course work with or alongside, is a good pre-med major.
Arizona’s engineering majors are listed here: http://engineering.arizona.edu/majors
If you are interested in them, you may want to find out what technical electives are allowed by each major in terms of being able to complete the remaining pre-med courses within them. Chemical engineering even has specific suggestions for pre-med students at http://www.chee.arizona.edu/undergraduates-options .