"It's a pretty broad agenda," press secretary Tony Snow, accompanying Bush on a trip to Philadelphia, told reporters.
The Russian was a guest of Bush and his father, the former President George H.W. Bush, at the elder Bush's Maine seaside resort home recently.
Snow said that Brown will arrive Sunday night and have dinner and meetings at Camp David, Maryland, on Monday, although he said he did not know if Bush and Brown planned a joint news conference there.
The two leaders have a "very special important relationship," Snow said. He said they were expected to talk about issues of "shared interest and concern," including the U.S. push to build a missile defense system in Eastern Europe, Iraq, Iran, Kosovo and Darfur.
Bush and Blair formed a close relationship as leaders in wartime, and Blair often was criticized for that at home.
British Foreign Secretary David Miliband stressed in a recent published commentary that the U.S. remains Britain's strongest ally despite the change of leadership in his country.
"With a new Brown government, some people are looking for evidence that our alliance is breaking up," Miliband wrote in the News of the World. "There isn't any and there won't be any.
"Nothing has changed. Our strongest bilateral relationship is with the U.S.A," he said.
The face of USA's First Lady Melania Trump after her handshake with Russian President Putin has received a lot of attention in social media
Moscow is trying to stop Balkan countries from entering NATO. Greece eventually took measures against Russia, even though Greek Prime Minister Alexis Tsipras had earlier said that Russia was Greece's strategic partner
The Ukrainian government refuses to abode by its obligations, rejects a peaceful resolution of the conflict, and disregards its own people, the president said