The Diamondbacks haven't asked for permission to interview Levine, but Rangers officials expect something to happen soon.
The Rangers have lost several front office people this year. Assistant GM A.J. Preller left this summer to become the GM of the San Diego Padres and he took Don Welke with him to work in the front office.
Levine, like Preller, is a trusted member of Texas' front office for GM Jon Daniels.
Rangers officials have always said when you have success on the field, other teams will try to hire their people.
The Diamondbacks fired GM Kevin Towers last week and have Hall of Famer manager Tony La Russa, their chief baseball officer, leading the search for his replacement.