Muller, who is fourth on Bayern Munich’s list of all-time top scorers, played a fringe role under Kovac earlier in the season.
Kovac was sacked in November after an underwhelming start to the season and replaced by Hansi Flick, who has reinvigorated Bayern Munich’s campaign.
Muller has regained his place in the Bayern first team since Flick’s appointment and he put pen-to-paper on a new two-year deal earlier this week.
However, the 30-year-old was not too hopeful of extending his 12-year association with Bayern Munich had Kovac remained at the helm.
"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."
Muller has scored six times and provided 12 assists in 15 Bundesliga games since Flick’s appointment.
Bayern Munich were four points clear at the top of the league table when Bundesliga was suspended because of Covid-19.
