Jeter, 39, said he's talked with Banks, 83, a few times.
"He treated me well when I was first coming up," Jeter said of Mr. Cub. "You always remember how someone makes you feel when you first meet them. I've always appreciated how he treated me."
Starlin Castro presented Jeter with the No. 2 at home plate prior to the series opener. Cubs players applauded, and fans gave Jeter a standing ovation.
The two shortstops talked briefly.
"He told me to keep playing hard and said I'm fun to watch," Castro said. "I said, 'Thank you.' You feel good when great people like that tell you that."
Cubs manager Rick Renteria saluted Jeter when asked about the shortstop.
"[He's the] ultimate, consummate professional," Renteria said. "Always solid preparation. I think of solid mindset. He's stuck around the league for a long time, and a Hall of Famer, obviously. He's been gifted with probably a great mind, great sense of the game, great work ethic, and those are things we see from the outside."
This was only Jeter's fourth game at Wrigley Field, and he may be OK with saying goodbye. He began the day 2-for-11 with three walks. Tuesday was the first of six straight games in Chicago for the Yankees, who next will play the White Sox at U.S. Cellular Field, starting Thursday.
"I like Chicago," Jeter said. "I've always enjoyed coming here. Besides baseball, my family used to come here on vacation when I was growing up, so I enjoy Chicago."
However, the visitor's clubhouse is tight compared to the new Yankee Stadium, and the dugouts are cramped.
"I like the history of the game," Jeter said. "Obviously, we get spoiled at home, the size of the clubhouse and all the amenities that are in the stadium. I'm a baseball historian, so I appreciate the fact that there's a lot of history that comes along with this ballpark. I'm happy that I get an opportunity to be here."
Yankees manager Joe Girardi said Jeter deserves the ovations he's received on the road.
"I think he's been a great ambassador for the game, and you hope that someone picks up the torch when he hands it off after this season," Girardi said. "The way he's been treated in each ballpark has been really nice, and I think when you see how he's treated in every ballpark, you don't forget how wonderful for the game he has been over the 19 years or whatever it's been. You really appreciate him."