While the Kenyan is reported to be looking to move to England, Forrest – also just 20 – has ignored the Premiership clubs tracking him.
Skipper Brown said: "I'd be surprised if Victor was thinking of leaving. You need a couple of seasons, especially at a club like this, to learn your trade.
"If you look at James Forrest, he has had a good two seasons, and his head has not gone through the roof.
"In terms of Victor, I think it is more paper talk than anything. He enjoys it here. So, hopefully, it is just that, paper talk."
Brown is also keen to see Fraser Forster sign the four-year deal on the table, and is confident there is enough on offer at Celtic to satisfy any player.
The captain reckons the only thing to match big Euro nights are Old Firm games, and has his fingers crossed they are not consigned to history.
Brown said: "It would be gutting if there were no more Rangers-Celtic games."
Brown sympathises with chairmen who will face a vote on keeping Rangers in the SPL and said: "It's quite a night-mare – to put it nicely.
"It's all about money, at the end of the day.
"It comes down to whether or not people bite their tongue and take it for two or three years with no Rangers or keep the money going into the stadiums."