The leaders will attend the exhibition game at London's Wembley stadium - likely to be hotly contested between the two soccer rivals - after discussions focussing on development and trade, officials said.
A Downing Street spokeswoman, speaking on customary condition of anonymity, said Merkel and Brown planned to discuss "international development issues, trade and other issues arising out of the G8."
She did not specify if Brown and Merkel planned further talks on climate change, the issue Germany made the centerpiece of its leadership of the Group of Eight industrialized nations, or efforts to meet targets to cut carbon dioxide levels.
The EU bloc has agreed to cut greenhouse gas emissions by 20 percent by 2020, while the G8 leaders agreed in June to call for substantial global emissions reductions, citing a goal of a 50 percent cut by 2050.
Brown made his first foreign visit as Britain's new prime minister to Germany in July.
The United States has always been the largest defense spender in the world with China following second. In 2017, Russia started losing its positions and dropped to the fourth place and then to the seventh, in 2019