Hendry and Pujols, who have been friendly for years, did have a brief embrace when they saw each other at Wrigley Field before the teams opened a three-game series. The embrace quickly was dubbed "The Hug."
The fact that Pujols will be a free agent next year likely fueled some of the coverage.
"Albert and I had always had a good relationship," Hendry told ESPNChicago.com on Wednesday. "I think the world of him, and that has nothing to do with what type of baseball player he is. I have all the respect in the world for him, way beyond him being a great player, and he knows that."
Hendry was shocked that the exchange made national news.
"I guess that's the world we live in," he said. "I've had a certain relationship with him for most of his career, and that's not going to change.
"Shame on me if he comes to town and we don't have a chat. I'm honored that he considers me that close."
Baseball has tampering rules preventing any team officials from conversing with players from other teams about their future or contract status. Fines and suspensions have been levied against owners and executives in the past.
Hendry said he got to know Pujols through former Cardinals general manager Walt Jocketty and former pitcher Alan Benes, who threw for Hendry at Creighton and for the Cardinals.
"I just try to be Jim Hendry. I don't have a game plan to talk to players or don't talk to players," Hendry said. "It's just who I am.
"He was very, very good to my son [John] when he was younger. We'll have a good relationship long after I'm done working in baseball and he's [done] playing."