In 2014, the National Institutes of Health invested $31 million in 10 primary institutions across the United States through the Building Undergraduate Infrastructure Leading to Diversity (BUILD) program; one requirement of BUILD is sending undergraduate trainees from those primary institutions to partner institutions for research experiences. Mechanisms like BUILD are designed to broaden research opportunities for students, especially those from underrepresented backgrounds. However, to our knowledge, no studies have examined faculty willingness to mentor undergraduates from other institutions through structured training programs. Survey data from 536 faculty members at 13 institutions were collected in Fall 2013 and analyzed using multiple statistical techniques. Results show that faculty who valued the opportunity to increase diversity in the academy and those who believed that mentoring undergraduates benefited their own research expressed greater willingness to serve as research mentors to visiting undergraduates, and faculty who perceived that they did not have the ability to accommodate additional students expressed less willingness to do so. Most respondents viewed student and faculty incentives as motivating factors in their willingness to mentor, but their perspectives on different types of incentives varied based on faculty career stage, discipline, and research funding status. Results have important implications for designing multi-institutional undergraduate research training programs.