Discussions with Bush would cap Cameron's rise from political novice to potential British prime minister, burnishing his statesman's credentials.
Cameron's staff hope Bush will agree to a request for a meeting during a White House visit Thursday.
"He hopes to meet senior administration officials," said a Conservative party spokeswoman, on condition of anonymity in line with party policy. "But we can't confirm or deny if he will meet with the president."
Talks could rehabilitate relations between the traditionally allied Republican and Conservative parties - a link that has waned as Bush embraced ex-Labour chief Tony Blair.
Russia, when signing documents for the sale of Alaska to the United States, was realizing her objective benefit
Putin's official spokesman Dmitry Peskov commented on remarks in the US media about failures in launching nuclear-capable missiles in Russia