Along with Cole Hamels, Prince Fielder and Derek Holland, Banister made the hour-long drive into Ann Arbor and spoke privately with Harbaugh before addressing his football team.
"Same message as I give our guys," Banister said. "It's about brotherhood; it's about playing for each other; it's about the sacrifices that you do make and the grit and grind that you go through on a daily basis -- how you learn from near-misses so that you're stronger."
Saturday wasn't the first time Banister has met with a prominent football coach. Earlier this month, when the Rangers were in Seattle for a series against the Mariners, he and his staff went to the Seahawks' training camp and interacted with Pete Carroll.
"You share thoughts and ideas in how to coach and messages, what the adversities are and how to overcome them," Banister said.
Holland, who grew up a Michigan fan despite his upbringing near Columbus, Ohio, drove to Ann Arbor on Friday as well as Saturday to watch the Wolverines practice. He and Banister both returned to Comerica Park with football helmets, gifts from the team.
"It takes you away from baseball and shows you how different the sport is," Holland said. "It was fun."
Harbaugh also may have gained the respect of Joey Prebynski, the Rangers video coordinator and scout who went to Ann Arbor with Holland on Friday.
Saturday afternoon, Prebynski -- an Ohio State supporter -- added a quote to the lineup card hanging in the Rangers clubhouse. It read: "'The Team, The Team, The Team.' -- Bo Schembechler."
"We are teaching, coaching and motivating athletes," Banister said of his respect for football coaches. "It may be a different sport, but it's still a team sport."
Alejandro Zúñiga is an associate reporter for MLB.com. Follow him on Twitter @ByAZuniga. This story was not subject to the approval of Major League Baseball or its clubs.