The Scotsman, who was replaced as manager by Rodgers following his sacking in 2012, returned to Anfield in a non-executive role on Friday.
"The most important person in me coming back was Brendan," the Liverpool Echo quotes Dalglish as saying. "The manager is more important than I am and his position was more important to me than my position.
"You could fully understand if the manager wasn't in agreement with it. If he wasn't, he would never have known I'd been asked.
"That was the most important thing for me, the fact that people within the club knew I was coming back and wanted me to come back and I wasn't standing on anybody's toes."