Brown is playing some of the best football of his career after a disappointing end to the last campaign, which ended prematurely for the 31-year-old amid hamstring problems.
The retired Scotland international scored the winner against Dundee on Saturday after shining in the 3-3 Champions League draw with Manchester City days earlier.
And the midfielder has credited manager Brendan Rodgers and his staff with playing a major role in his revival in fortunes.
Brown told the Evening Times: “I think it all starts going into training. The training has been great, as have the physios and coaches.
“It wasn’t always like that last year. It didn’t always put a smile on your face when going into training. It was difficult, it was slow, the training itself wasn’t hard enough.
“This season, all the lads are enjoying it, they want to work hard. It doesn’t matter if it’s Monday, Tuesday, Wednesday, Thursday or Friday; training has been exceptional.”
Meanwhile, Kenny Dalglish believes Rodgers can already regard his first season a success.
The former Celtic striker and manager feels his old club are certainties to claim their sixth consecutive Scottish title having already achieved their main European aim.
Dalglish, who was unveiling the William Hill Stand at Hampden, said: “It’s been a great start. They got qualification into the Champions League, which I think would ensure that that’s success for Celtic this year.
“The expectation is for them to win the league. I think you could award them that now. I think they will go on and win the league comfortably.
“Who knows what’s going to happen long term but it’s been a great start.”
Dalglish, who was succeeded as Liverpool manager by Rodgers, added: “As he said when he came, you don’t realise how big the club is until you work there. It’s massive.
“For Scottish football, I think it’s also equally as important that they have rivals that can push them a bit closer, without taking the success away from them.
“The level they rose to against Manchester City, if they got to play week in, week out against teams that push them harder, then that performance wouldn’t just be a one-off.
“But a big result for them was coming back after the Man City game and winning 1-0 against Dundee, because Man City must have taken a lot out of them.”
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