The two clubs played out several memorable battles earlier this decade when they were the dominant forces in the competition.
The Lions won finals against Port Adelaide in 2001 and 2002 on the way to the flag premierships before the Power exacted revenge on the biggest stage two years later to claim their first premiership.
Brown said he and the other Lions senior players had long memories.
“There’s plenty of hatred between the Lions and Port Adelaide over the years,” he said.
“They always seemed to be one-point and six-point games and there used to be plenty of animosity and physicality in those contests.
“We played in some finals and they beat us on the ultimate stage in 2004 and that was hard to stomach because that was the biggest rivalry at the time along with Collingwood.
“For myself and some of the older guys there’s still plenty of passion against them.”
Brown said Port Adelaide’s s “very, very passionate” supporters would provide a great challenge for the Lions, who head into the game with an 8-5 record.
After successive five-goal hauls, the All-Australian forward leads the race for the Coleman Medal with 45 majors but he said he had bigger fish to fry in 2009 than chasing individual glory.
“Individually, we can’t deny we want to play well, but my major motivating factor is trying to play finals football,” he said.
“It’s selfish, but I know what it’s like to be in successful teams, and when you go from thinking it’s normal to play in grand finals to not even making finals, it starts to get frustrating and it’s a big driving force for me.
“No doubt we want to make finals but at the moment we want to get to those 12 wins.
“There’s no question as you get older – I’m only 27 but I’m in my 10th year – you get a little more desperate to experience that again.
“It’s a constant evolution of the team and you hope the club drafts well and we have, we have a terrific bunch of young blokes at the moment.”
While praising the club’s youngsters, Brown said one of the biggest areas of improvement for the Lions this season had been their forward line.
While he and Daniel Bradshaw (34) have still kicked the majority of the team’s goals, the scoreboard contributions have been plentiful from elsewhere.
“We copped a lot of flak at the end of last season because me and Braddy kicked over half our goals and there was only about six goalkickers a game and that’s not the spread we were looking for,” he said.
“There’s no doubt we’ve got a focus on more guys kicking goals. We may have had too big a focus on defensive pressure ... but your main function as a forward is to kick goals, and that’s been a change of focus for us.
“We’ve got more options in the forward line now. James Polkinghorne has been fantastic, almost in a pseudo key forward role, and we have guys like Rischitelli going through there, Albert Proud has been great, (Rhan) Hooper’s back, (Daniel) Rich is kicking goals and (Justin) Sherman has re-emerged and I think that’s one of the biggest factors to our success so far.”