The veteran Rangers striker was speaking ahead of his side’s curtain-raiser against Hamilton on Saturday.
The Gers’ season opener will see them return to top flight action for the first time in four years against the Accies.
Earlier this week, Hoops skipper Brown wrote off the Ibrox side’s title chances ahead of the new campaign – and claimed that Aberdeen or Hearts would be the closest challengers.
But today Miller has hit back at Brown, insisting the Celts captain only said it to noise-up their rivals and grab the headlines.
He said, via stv.tv: “That’s only going to be motivation for Aberdeen and for Hearts who aren’t even getting mentioned.
“You take that with a pinch of salt. There’s no way that Scott Brown actually believes that.
“He’s saying that to get a headline and noise people up.”
Gers forward Miller also reckons last season’s Scottish Cup semi-final win – which saw Mark Warburton’s men go through on a dramatic penalty shootout – shows just how much of a problem they can cause Brendan Rodgers’ side.
Miller said: “Let’s be honest about it, he knows from the semi-final last year where we won on penalties but we dominated that game.
“We were worthy winners and if we didn’t win it in normal time it should have been extra time.”
“He knows the challenge that we’re going to bring them this season.
“Again, I don’t think Broony got his own scores against Aberdeen right at Parkhead.
“He said they came to Parkhead and got points but they never, so we will take that with a pinch of salt as well.”
The first Old Firm of the season is set to be played at Parkhead on September 10.
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