The 24-year old striker scored his 16th goal of the season in all competitions as the Hoops beat Dundee 2-0 on Boxing Day and Brown believes the next step for the former Scunthorpe United man is an international berth.
"I don't think Gary can be far away from an England call-up," he said.
"He's playing in the hole because we've got a few injuries and that shows you he can play anywhere.
"He creates his chances and scores goals. The finish he came up with here was just ridiculous.
"He's definitely good enough to play for England. They are looking for a striker.
"I know Wayne Rooney plays in that hole as well, but Gary could easily play up front for England."