Manchester United midfielder Pogba has at times struggled to match up to his £89m transfer fee.
The France international has endured two mixed seasons at Old Trafford since his then-world record breaking move from Juventus.
Barcelona are reported to be interested in Pogba, whose French team won the World Cup this summer.
But Brown reckons the 25-year-old will shine in the Premier League this season, using the World Cup as a springboard to boost his domestic performances.
“Pogba came back to United with this great expectation, that he had to show the world how good he is straight away,” Brown said.
“A lot of pressure comes with that”.
“With that out of the way he’s coming good though we all know he can do even better.
“This season, especially after the World Cup that he’s had, he’s going to start expressing himself a lot more.”
Barcelona are said to be keen on getting Manchester United midfielder Pogba before the Spanish transfer window closes on August 31.
However, United are very unlikely to sell their key midfielder with the Premier League transfer deadline coming on Thursday.
A move to the Nou Camp would most likely be delayed until next summer, although United would still demand at least the £89m spent on Pogba before considering letting him leave.