Former Germany forward Muller penned fresh terms at the Allianz Arena to run until June 2023 this week.
The 30-year-old will be forever synonymous with Bayern and sits fourth on their all-time scoring charts with 195 goals across 521 appearances.
However, he found himself out in the cold under Kovac, who was sacked in November.
Since Hansi Flick's arrival, initially as an interim head coach, Muller has been a player revitalized, netting six goals and supplying a remarkable 12 assists in 15 Bundesliga games.
"In autumn, I was left out of the starting 11 for six games in a row. It was difficult. Of course, it made me think," he told an online news conference on Thursday.
"Emotionally, it was very tense back then. I wasn't necessarily thinking that I would be extending my contract in the spring.
"With the change of coach and different playing style, everything has developed positively.
"Not only have I been playing more, but I've also been able to put my stamp on our games again."
Bayern's players returned to training in small groups on Monday, with the club offering assurances that "all hygiene regulations will be strictly observed" amid the ongoing coronavirus pandemic.
"We try to stick to what is specified from above," Muller said. "I don't know what is specified and restricted in other areas.
"We have to fit into the overall structure. I don't know if football has a special position."
He added: "We all want to play football, of course, but only from the point of view that makes sense. This is an exceptional situation, not only for football."