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.
Malaysia needs Russia's assistance in maintaining and repairing Su-30MKM fighter jets