The 20-year old winger produced a two-goal performance as the Hoops beat Motherwell 4-0 on the weekend and that has sparked comparisons with former Celtic star Aiden McGeady, currently with Russian club Spartak Moscow.
Brown feels Forrest has plenty to offer and can see a lot if improvement from the youngster who has been capped twice by the Scotland senior team.
"The gaffer knows what Jamesy can do,” Brown said.
"He is a great player and he's probably the most exciting player to come through in Scotland since Aiden McGeady. He gives you pace and goals as well.
"He is adding a lot to his game as he gets older and, for a lad of his age, he has a great career ahead of him.
"When I was a young lad coming through, it was just great to be playing at this level.
"I think this season will be big for him, every season will be.
"Jamesy is very laid back and down to earth. He's a nice guy, who is quite quiet off the park.
"There is nothing in his lifestyle that is going to cause a problem or go to his head, that's for sure.
"I'm sure there were a few players in the past who came through and went the other way — but Jamesy is different.
"He enjoys coming into training, enjoys learning and enjoys playing football.
"That's his focus and he is a great guy to play alongside. He is working on his deliveries and scoring goals and those aspects are coming off for him."