The midfielder came though the ranks at Easter Road and picked up a League Cup winners medal before signing for the Parkhead club in 2007 for a reported £4.4million. However, Scottish Cup success eluded him as it has Hibs players since a 1-0 win over the Hoops in 1902.
Speaking at the national stadium, Brown, 27, was asked if he was aware of a desperation among the Hibs fans to end that hoodoo during his time at the Edinburgh club.
"Yes," he replied. "Every season it went on an extra year and it keeps going but hopefully it goes on another extra year for them, that's for sure.
"It is going to be a huge occasion for them. It is going to be a battle. It is going to be hard for us and hard for them as well.
"It has been a long time since they won it but we want to get our hands on it as well."
Hibs' more recent final appearance ended in calamity when they lost 5-1 to Edinburgh neighbours Hearts in last year's final.
Brown, who eventually got his hands on the trophy after Celtic beat Motherwell 3-0 two seasons ago, believes Pat Fenlon's side will be travelling to Mount Florida on Sunday seeking redemption.
"Yes, definitely, they have a huge point to prove," said the Scotland midfielder. "It was a sore one for every Hibs player and every Hibs fan last season.
"They have come back in good spirits all the way again but I just hope it is our cup this year."