Russia's recent downturn in relations with the UK and the US could also come up.
In a statement on the eve of his visit, Brown said the British-American relationship was "founded on our common values of liberty, opportunity and the dignity of the individual".
"And because of the values we share, the relationship with the United States is not only strong, but can become stronger in the years ahead," he said.
But observers say Brown's relationship with Bush will not be as close as that of his predecessor, Tony Blair.
Brown, a critic of the Iraq war, would try to repair Britain's international image damaged by its involvement in the war, but would have to balance that with not destabilising his country's close economic and security ties with the US, they say.
There is already concern in Washington over some of Brown's cabinet appointments, but the US says Britain remains its strongest foreign ally.